%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU627^1 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:35:42 AM UTC 2026
% Result : Theorem 78.40s 12.31s
% Output : Refutation 78.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 24
% Syntax : Number of formulae : 143 ( 33 unt; 0 typ; 2 def)
% Number of atoms : 3743 ( 987 equ; 0 cnn)
% Maximal formula atoms : 149 ( 26 avg)
% Number of connectives : 2915 ( 248 ~; 181 |; 510 &;1342 @)
% ( 18 <=>; 616 =>; 0 <=; 0 <~>)
% Maximal formula depth : 159 ( 12 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 294 ( 291 usr; 174 con; 0-4 aty)
% Number of variables : 301 ( 0 ^; 219 !; 82 ?; 301 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
exu: ( $i > $o ) > $o ).
thf(func_def_6,type,
setadjoin: $i > $i > $i ).
thf(func_def_8,type,
powerset: $i > $i ).
thf(func_def_10,type,
setunion: $i > $i ).
thf(func_def_19,type,
descr: ( $i > $o ) > $i ).
thf(func_def_21,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_26,type,
prop2set: $o > $i ).
thf(func_def_36,type,
nonempty: $i > $o ).
thf(func_def_69,type,
set2prop: $i > $o ).
thf(func_def_88,type,
subset: $i > $i > $o ).
thf(func_def_89,type,
disjoint: $i > $i > $o ).
thf(func_def_90,type,
setsmeet: $i > $i > $o ).
thf(func_def_114,type,
binunion: $i > $i > $i ).
thf(func_def_122,type,
binintersect: $i > $i > $i ).
thf(func_def_135,type,
regular: $i > $o ).
thf(func_def_136,type,
setminus: $i > $i > $i ).
thf(func_def_147,type,
symdiff: $i > $i > $i ).
thf(func_def_153,type,
iskpair: $i > $o ).
thf(func_def_158,type,
kpair: $i > $i > $i ).
thf(func_def_160,type,
cartprod: $i > $i > $i ).
thf(func_def_181,type,
sP1: $i > $i > $o ).
thf(func_def_182,type,
sP2: $i > $o ).
thf(func_def_183,type,
sP3: $i > $i > $o ).
thf(func_def_184,type,
sP4: $i > $i > $o ).
thf(func_def_185,type,
sP5: $i > $i > $i > $o > $o ).
thf(func_def_190,type,
sK10: $i > $o ).
thf(func_def_192,type,
sK12: ( $i > $o ) > $i > $i ).
thf(func_def_196,type,
sK16: $i > $i > $i ).
thf(func_def_200,type,
sK20: $i > ( $i > $o ) > $i ).
thf(func_def_201,type,
sK21: $i > $o ).
thf(func_def_203,type,
sK23: $i > $i > $i ).
thf(func_def_206,type,
sK26: $i > $o ).
thf(func_def_207,type,
sK27: $i > $i ).
thf(func_def_208,type,
sK28: ( $i > $o ) > $i ).
thf(func_def_217,type,
sK37: $i > $i > $i ).
thf(func_def_224,type,
sK44: $i > $o ).
thf(func_def_228,type,
sK48: $i > $o ).
thf(func_def_241,type,
sK61: $i > $o ).
thf(func_def_246,type,
sK66: $i > $i > $i ).
thf(func_def_249,type,
sK69: $i > $o ).
thf(func_def_252,type,
sK72: $i > ( $i > $o ) > $i ).
thf(func_def_254,type,
sK74: $i > $o ).
thf(func_def_263,type,
sK83: $i > $i ).
thf(func_def_267,type,
sK87: $i > $i ).
thf(func_def_269,type,
sK89: $i > $i ).
thf(func_def_273,type,
sK93: $i > $i > $i ).
thf(func_def_274,type,
sK94: $i > $i > $o ).
thf(func_def_276,type,
sK96: $i > $i ).
thf(func_def_277,type,
sK97: $i > $i ).
thf(func_def_278,type,
sK98: $i > ( $i > $i > $o ) > $i ).
thf(func_def_279,type,
sK99: $i > ( $i > $i > $o ) > $i ).
thf(func_def_280,type,
sK100: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_283,type,
sK103: $i > $o ).
thf(func_def_286,type,
sK106: $i > $o ).
thf(func_def_301,type,
sK121: $i > $o ).
thf(func_def_321,type,
sK141: $i > ( $i > $o ) > $i ).
thf(func_def_322,type,
sK142: $i > $o ).
thf(func_def_327,type,
sK147: $i > $o ).
thf(func_def_330,type,
sK150: $i > ( $i > $o ) > $i ).
thf(func_def_331,type,
sK151: $i > $o ).
thf(func_def_353,type,
sK173: $i > $o ).
thf(func_def_355,type,
sK175: ( $i > $o ) > $i ).
thf(func_def_356,type,
sK176: ( $i > $o ) > $i ).
thf(func_def_358,type,
sK178: $i > $i ).
thf(func_def_361,type,
sK181: $i > $o ).
thf(func_def_362,type,
sK182: $i > $o ).
thf(func_def_363,type,
sK183: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_364,type,
sK184: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_381,type,
sK201: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_382,type,
sK202: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_383,type,
sK203: $i > $o ).
thf(func_def_384,type,
sK204: $i > $o ).
thf(func_def_387,type,
sK207: $i > $i ).
thf(func_def_389,type,
sK209: $i > $i > $i ).
thf(func_def_390,type,
sK210: $i > $i > $i ).
thf(func_def_391,type,
sK211: $i > $i > $i ).
thf(func_def_392,type,
sK212: $i > $i > $i ).
thf(func_def_393,type,
sK213: $i > $i > $i > $i ).
thf(func_def_394,type,
sK214: $i > $i ).
thf(func_def_395,type,
sK215: $i > $i ).
thf(func_def_396,type,
sK216: $i > $i ).
thf(func_def_397,type,
sK217: $i > $i ).
thf(func_def_398,type,
sK218: $i > $i > $i > $i ).
thf(func_def_399,type,
sK219: $i > $i > $i > $i ).
thf(func_def_400,type,
sK220: $i > $i > $i ).
thf(func_def_401,type,
sK221: $i > $i > $i ).
thf(func_def_402,type,
sK222: $i > $i > $i ).
thf(func_def_404,type,
sK224: $i > $i ).
thf(func_def_405,type,
sK225: $i > $i ).
thf(func_def_406,type,
sK226: $i > $i ).
thf(func_def_407,type,
sK227: $i > $i > $i ).
thf(func_def_411,type,
sK231: $i > $o ).
thf(func_def_417,type,
sK237: $i > $i ).
thf(func_def_452,type,
sK272: $i > $o ).
thf(func_def_455,type,
sK275: ( $i > $o ) > $i ).
thf(func_def_456,type,
sK276: $i > $o ).
thf(func_def_457,type,
sK277: $i > $o ).
thf(func_def_460,type,
sK280: $i > ( $i > $o ) > $i ).
thf(func_def_461,type,
sK281: $i > $o ).
thf(func_def_475,type,
sK295: $i > $o ).
thf(func_def_482,type,
sK302: $o > $i > $i > $i ).
thf(func_def_485,type,
sK305: $i > $i > $i ).
thf(func_def_517,type,
sK337: $i > $i > $i ).
thf(func_def_518,type,
sK338: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_519,type,
sK339: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_520,type,
sK340: $i > $o ).
thf(func_def_521,type,
sK341: $i > $o ).
thf(func_def_534,type,
sK354: $i > $o ).
thf(func_def_537,type,
sK357: $i > ( $i > $o ) > $i ).
thf(func_def_555,type,
sK375: $i > $i ).
thf(func_def_558,type,
sK378: $i > $o ).
thf(func_def_561,type,
sK381: $i > ( $i > $o ) > $i ).
thf(func_def_565,type,
sK385: $i > $i > $i ).
thf(func_def_566,type,
sK386: $i > $i > $i ).
thf(func_def_572,type,
sK392: ( $i > $o ) > $i ).
thf(func_def_573,type,
sK393: $i > $o ).
thf(func_def_574,type,
sK394: $i > $i ).
thf(func_def_576,type,
ph396:
!>[X0: $tType] : X0 ).
thf(f9113,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f8593,f8880,f9111]) ).
thf(f9111,plain,
~ spl395_14,
inference(avatar_contradiction_clause,[status(thm)],[f9110]) ).
thf(f9110,plain,
( $false
| ~ spl395_14 ),
inference(subsumption_resolution,[status(thm)],[f9109,f1566]) ).
thf(f1566,plain,
upairsubunion = $true,
inference(cnf_transformation,[status(thm)],[f834]) ).
thf(f834,plain,
( ( subsetRefl = $true )
& ( symdiffIneg1 = $true )
& ( exuI3 = $true )
& ( subPowSU = $true )
& ( symdiffI1 = $true )
& ( setminusER = $true )
& ( setoftrueEq = $true )
& ( dsetconstrER = $true )
& ( binunionE = $true )
& ( nonemptyE1 = $true )
& ( nonemptyI = $true )
& ( uniqinunit = $true )
& ( setadjoinOr = $true )
& ( disjointsetsI1 = $true )
& ( binunionIR = $true )
& ( subsetE = $true )
& ( setminusIRneg = $true )
& ( exuI1 = $true )
& ( inCongP = $true )
& ( singletonsswitch = $true )
& ( emptyInPowerset = $true )
& ( foundationAx = $true )
& ( setadjoinIL = $true )
& ( wellorderingAx = $true )
& ( powersetsubset = $true )
& ( subset2powerset = $true )
& ( descrp = $true )
& ( emptysetimpfalse = $true )
& ( upairset2IR = $true )
& ( binintersectEL = $true )
& ( setminusI = $true )
& ( subsetE2 = $true )
& ( subsetI2 = $true )
& ( notequalI2 = $true )
& ( in__Cong = $true )
& ( setukpairIR = $true )
& ( singletoninpowerset = $true )
& ( kpairiskpair = $true )
& ( notsubsetI = $true )
& ( exuI2 = $true )
& ( exuE3e = $true )
& ( notinemptyset = $true )
& ( upairsubunion = $true )
& ( setunionAx = $true )
& ( subsetTrans = $true )
& ( setminusILneg = $true )
& ( binintersectRsub = $true )
& ( powersetAx = $true )
& ( emptyI = $true )
& ( quantDeMorgan2 = $true )
& ( omega0Ax = $true )
& ( upairinpowunion = $true )
& ( replAx = $true )
& ( emptysetE = $true )
& ( binintersectSubset1 = $true )
& ( omegaIndAx = $true )
& ( binunionRsub = $true )
& ( binintersectI = $true )
& ( prop2setE = $true )
& ( symdiffE = $true )
& ( powersetE = $true )
& ( setadjoinIR = $true )
& ( nonemptyI1 = $true )
& ( eqimpsubset1 = $true )
& ( subsetI1 = $true )
& ( setminusLsub = $true )
& ( eqimpsubset2 = $true )
& ( setminusSubset2 = $true )
& ( setunionE = $true )
& ( setadjoinE = $true )
& ( emptysetAx = $true )
& ( emptyinPowerset = $true )
& ( exuEu = $true )
& ( singletoninpowunion = $true )
& ( notinsingleton = $true )
& ( setunion__Cong = $true )
& ( subsetemptysetimpeq = $true )
& ( descr__Cong = $true )
& ( upairsetE = $true )
& ( prop2set2propI = $true )
& ( binintersectSubset5 = $true )
& ( setunionI = $true )
& ( binunionIL = $true )
& ( setadjoinSub2 = $true )
& ( powerset__Cong = $true )
& ( binintersectER = $true )
& ( prop2setI = $true )
& ( upairset2E = $true )
& ( exuE3u = $true )
& ( notequalI1 = $true )
& ( exuE1 = $true )
& ( setminusERneg = $true )
& ( setadjoinSub = $true )
& ( quantDeMorgan3 = $true )
& ( upairsetIL = $true )
& ( binunionEcases = $true )
& ( emptysetsubset = $true )
& ( binintersectLsub = $true )
& ( kpairp = $true )
& ( quantDeMorgan1 = $true )
& ( powersetE1 = $true )
& ( vacuousDall = $true )
& ( dsetconstrEL = $true )
& ( omega__Cong = $true )
& ( noeltsimpempty = $true )
& ( setminusEL = $true )
& ( setminusSubset1 = $true )
& ( setadjoinAx = $true )
& ( emptyset__Cong = $true )
& ( inPowerset = $true )
& ( omegaSAx = $true )
& ( dsetconstr__Cong = $true )
& ( emptyinunitempty = $true )
& ( sepInPowerset = $true )
& ( powersetI1 = $true )
& ( bs114d = $true )
& ( binintersectSubset2 = $true )
& ( setukpairIL = $true )
& ( setextsub = $true )
& ( setext = $true )
& ( setadjoin__Cong = $true )
& ( symdiffIneg2 = $true )
& ( powersetI = $true )
& ( symdiffI2 = $true )
& ( singletonsubset = $true )
& ( binintersectSubset3 = $true )
& ( quantDeMorgan4 = $true )
& ( nonemptyImpWitness = $true )
& ( setextAx = $true )
& ( setminusELneg = $true )
& ( dsetconstrI = $true )
& ( notdexE = $true )
& ( upairsetIR = $true )
& ( setbeta = $true )
& ( eqinunit = $true )
& ( emptyE1 = $true )
& ( exuE2 = $true )
& ( sepSubset = $true )
& ( exu__Cong = $true )
& ( notdallE = $true )
& ( $true
!= ( subset @ ( setadjoin @ ( setadjoin @ sK125 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK125 @ ( setadjoin @ sK128 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ sK126 @ sK127 ) ) ) )
& ( ( in @ sK128 @ sK127 )
= $true )
& ( ( in @ sK125 @ sK126 )
= $true )
& ( binunionLsub = $true )
& ( secondinupair = $true )
& ( binintersectSubset4 = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK125,sK126,sK127,sK128])],[f587,f833,f832]) ).
thf(f832,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ? [X3: $i] :
( ( $true
!= ( subset @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
& ( ( in @ X3 @ X2 )
= $true ) )
& ( ( in @ X0 @ X1 )
= $true ) )
=> ( ? [X3: $i] :
( ( ( subset @ ( setadjoin @ ( setadjoin @ sK125 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK125 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ sK126 @ sK127 ) ) )
!= $true )
& ( ( in @ X3 @ sK127 )
= $true ) )
& ( ( in @ sK125 @ sK126 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f833,plain,
( ? [X3: $i] :
( ( ( subset @ ( setadjoin @ ( setadjoin @ sK125 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK125 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ sK126 @ sK127 ) ) )
!= $true )
& ( ( in @ X3 @ sK127 )
= $true ) )
=> ( ( $true
!= ( subset @ ( setadjoin @ ( setadjoin @ sK125 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK125 @ ( setadjoin @ sK128 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ sK126 @ sK127 ) ) ) )
& ( ( in @ sK128 @ sK127 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f587,plain,
( ( subsetRefl = $true )
& ( symdiffIneg1 = $true )
& ( exuI3 = $true )
& ( subPowSU = $true )
& ( symdiffI1 = $true )
& ( setminusER = $true )
& ( setoftrueEq = $true )
& ( dsetconstrER = $true )
& ( binunionE = $true )
& ( nonemptyE1 = $true )
& ( nonemptyI = $true )
& ( uniqinunit = $true )
& ( setadjoinOr = $true )
& ( disjointsetsI1 = $true )
& ( binunionIR = $true )
& ( subsetE = $true )
& ( setminusIRneg = $true )
& ( exuI1 = $true )
& ( inCongP = $true )
& ( singletonsswitch = $true )
& ( emptyInPowerset = $true )
& ( foundationAx = $true )
& ( setadjoinIL = $true )
& ( wellorderingAx = $true )
& ( powersetsubset = $true )
& ( subset2powerset = $true )
& ( descrp = $true )
& ( emptysetimpfalse = $true )
& ( upairset2IR = $true )
& ( binintersectEL = $true )
& ( setminusI = $true )
& ( subsetE2 = $true )
& ( subsetI2 = $true )
& ( notequalI2 = $true )
& ( in__Cong = $true )
& ( setukpairIR = $true )
& ( singletoninpowerset = $true )
& ( kpairiskpair = $true )
& ( notsubsetI = $true )
& ( exuI2 = $true )
& ( exuE3e = $true )
& ( notinemptyset = $true )
& ( upairsubunion = $true )
& ( setunionAx = $true )
& ( subsetTrans = $true )
& ( setminusILneg = $true )
& ( binintersectRsub = $true )
& ( powersetAx = $true )
& ( emptyI = $true )
& ( quantDeMorgan2 = $true )
& ( omega0Ax = $true )
& ( upairinpowunion = $true )
& ( replAx = $true )
& ( emptysetE = $true )
& ( binintersectSubset1 = $true )
& ( omegaIndAx = $true )
& ( binunionRsub = $true )
& ( binintersectI = $true )
& ( prop2setE = $true )
& ( symdiffE = $true )
& ( powersetE = $true )
& ( setadjoinIR = $true )
& ( nonemptyI1 = $true )
& ( eqimpsubset1 = $true )
& ( subsetI1 = $true )
& ( setminusLsub = $true )
& ( eqimpsubset2 = $true )
& ( setminusSubset2 = $true )
& ( setunionE = $true )
& ( setadjoinE = $true )
& ( emptysetAx = $true )
& ( emptyinPowerset = $true )
& ( exuEu = $true )
& ( singletoninpowunion = $true )
& ( notinsingleton = $true )
& ( setunion__Cong = $true )
& ( subsetemptysetimpeq = $true )
& ( descr__Cong = $true )
& ( upairsetE = $true )
& ( prop2set2propI = $true )
& ( binintersectSubset5 = $true )
& ( setunionI = $true )
& ( binunionIL = $true )
& ( setadjoinSub2 = $true )
& ( powerset__Cong = $true )
& ( binintersectER = $true )
& ( prop2setI = $true )
& ( upairset2E = $true )
& ( exuE3u = $true )
& ( notequalI1 = $true )
& ( exuE1 = $true )
& ( setminusERneg = $true )
& ( setadjoinSub = $true )
& ( quantDeMorgan3 = $true )
& ( upairsetIL = $true )
& ( binunionEcases = $true )
& ( emptysetsubset = $true )
& ( binintersectLsub = $true )
& ( kpairp = $true )
& ( quantDeMorgan1 = $true )
& ( powersetE1 = $true )
& ( vacuousDall = $true )
& ( dsetconstrEL = $true )
& ( omega__Cong = $true )
& ( noeltsimpempty = $true )
& ( setminusEL = $true )
& ( setminusSubset1 = $true )
& ( setadjoinAx = $true )
& ( emptyset__Cong = $true )
& ( inPowerset = $true )
& ( omegaSAx = $true )
& ( dsetconstr__Cong = $true )
& ( emptyinunitempty = $true )
& ( sepInPowerset = $true )
& ( powersetI1 = $true )
& ( bs114d = $true )
& ( binintersectSubset2 = $true )
& ( setukpairIL = $true )
& ( setextsub = $true )
& ( setext = $true )
& ( setadjoin__Cong = $true )
& ( symdiffIneg2 = $true )
& ( powersetI = $true )
& ( symdiffI2 = $true )
& ( singletonsubset = $true )
& ( binintersectSubset3 = $true )
& ( quantDeMorgan4 = $true )
& ( nonemptyImpWitness = $true )
& ( setextAx = $true )
& ( setminusELneg = $true )
& ( dsetconstrI = $true )
& ( notdexE = $true )
& ( upairsetIR = $true )
& ( setbeta = $true )
& ( eqinunit = $true )
& ( emptyE1 = $true )
& ( exuE2 = $true )
& ( sepSubset = $true )
& ( exu__Cong = $true )
& ( notdallE = $true )
& ? [X0: $i,X1: $i,X2: $i] :
( ? [X3: $i] :
( ( $true
!= ( subset @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
& ( ( in @ X3 @ X2 )
= $true ) )
& ( ( in @ X0 @ X1 )
= $true ) )
& ( binunionLsub = $true )
& ( secondinupair = $true )
& ( binintersectSubset4 = $true ) ),
inference(flattening,[status(thm)],[f586]) ).
thf(f586,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ? [X3: $i] :
( ( $true
!= ( subset @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
& ( ( in @ X3 @ X2 )
= $true ) )
& ( ( in @ X0 @ X1 )
= $true ) )
& ( upairinpowunion = $true )
& ( upairsubunion = $true )
& ( upairset2E = $true )
& ( singletoninpowunion = $true )
& ( singletoninpowerset = $true )
& ( singletonsubset = $true )
& ( kpairp = $true )
& ( kpairiskpair = $true )
& ( setukpairIR = $true )
& ( setukpairIL = $true )
& ( secondinupair = $true )
& ( symdiffIneg2 = $true )
& ( symdiffIneg1 = $true )
& ( symdiffI2 = $true )
& ( symdiffI1 = $true )
& ( symdiffE = $true )
& ( setminusSubset1 = $true )
& ( setminusLsub = $true )
& ( setminusIRneg = $true )
& ( setminusILneg = $true )
& ( setminusELneg = $true )
& ( setminusERneg = $true )
& ( setminusSubset2 = $true )
& ( setminusER = $true )
& ( setminusEL = $true )
& ( setminusI = $true )
& ( bs114d = $true )
& ( binintersectSubset1 = $true )
& ( binintersectSubset4 = $true )
& ( binintersectRsub = $true )
& ( disjointsetsI1 = $true )
& ( binintersectER = $true )
& ( binintersectSubset3 = $true )
& ( binintersectSubset2 = $true )
& ( binintersectLsub = $true )
& ( binintersectEL = $true )
& ( binintersectSubset5 = $true )
& ( binintersectI = $true )
& ( binunionRsub = $true )
& ( binunionLsub = $true )
& ( binunionE = $true )
& ( binunionEcases = $true )
& ( binunionIR = $true )
& ( upairset2IR = $true )
& ( binunionIL = $true )
& ( sepSubset = $true )
& ( sepInPowerset = $true )
& ( powersetsubset = $true )
& ( inPowerset = $true )
& ( powersetE1 = $true )
& ( powersetI1 = $true )
& ( subsetemptysetimpeq = $true )
& ( setextsub = $true )
& ( subset2powerset = $true )
& ( setadjoinSub2 = $true )
& ( setadjoinSub = $true )
& ( subsetTrans = $true )
& ( subsetRefl = $true )
& ( notequalI2 = $true )
& ( notequalI1 = $true )
& ( notsubsetI = $true )
& ( subsetE2 = $true )
& ( subsetE = $true )
& ( emptysetsubset = $true )
& ( subsetI2 = $true )
& ( eqimpsubset1 = $true )
& ( eqimpsubset2 = $true )
& ( subsetI1 = $true )
& ( dsetconstr__Cong = $true )
& ( descr__Cong = $true )
& ( exuEu = $true )
& ( omega__Cong = $true )
& ( setunion__Cong = $true )
& ( powerset__Cong = $true )
& ( setadjoin__Cong = $true )
& ( emptyset__Cong = $true )
& ( exu__Cong = $true )
& ( exuE3u = $true )
& ( in__Cong = $true )
& ( inCongP = $true )
& ( exuI2 = $true )
& ( exuI3 = $true )
& ( exuI1 = $true )
& ( notdallE = $true )
& ( notdexE = $true )
& ( prop2set2propI = $true )
& ( prop2setI = $true )
& ( quantDeMorgan4 = $true )
& ( quantDeMorgan3 = $true )
& ( quantDeMorgan2 = $true )
& ( quantDeMorgan1 = $true )
& ( vacuousDall = $true )
& ( emptyE1 = $true )
& ( upairsetIR = $true )
& ( upairsetIL = $true )
& ( upairsetE = $true )
& ( singletonsswitch = $true )
& ( eqinunit = $true )
& ( notinsingleton = $true )
& ( uniqinunit = $true )
& ( nonemptyImpWitness = $true )
& ( exuE2 = $true )
& ( subPowSU = $true )
& ( setunionE = $true )
& ( setunionI = $true )
& ( powersetE = $true )
& ( emptyInPowerset = $true )
& ( emptyinPowerset = $true )
& ( powersetI = $true )
& ( setoftrueEq = $true )
& ( setadjoinOr = $true )
& ( setadjoinE = $true )
& ( setadjoinIR = $true )
& ( emptyinunitempty = $true )
& ( setadjoinIL = $true )
& ( nonemptyI1 = $true )
& ( nonemptyI = $true )
& ( nonemptyE1 = $true )
& ( setbeta = $true )
& ( noeltsimpempty = $true )
& ( emptyI = $true )
& ( setext = $true )
& ( exuE3e = $true )
& ( notinemptyset = $true )
& ( emptysetimpfalse = $true )
& ( emptysetE = $true )
& ( prop2setE = $true )
& ( exuE1 = $true )
& ( dsetconstrER = $true )
& ( dsetconstrEL = $true )
& ( dsetconstrI = $true )
& ( descrp = $true )
& ( wellorderingAx = $true )
& ( foundationAx = $true )
& ( replAx = $true )
& ( omegaIndAx = $true )
& ( omegaSAx = $true )
& ( omega0Ax = $true )
& ( setunionAx = $true )
& ( powersetAx = $true )
& ( setadjoinAx = $true )
& ( emptysetAx = $true )
& ( setextAx = $true ) ),
inference(ennf_transformation,[status(thm)],[f252]) ).
thf(f252,plain,
~ ( ( setextAx = $true )
=> ( ( emptysetAx = $true )
=> ( ( setadjoinAx = $true )
=> ( ( powersetAx = $true )
=> ( ( setunionAx = $true )
=> ( ( omega0Ax = $true )
=> ( ( omegaSAx = $true )
=> ( ( omegaIndAx = $true )
=> ( ( replAx = $true )
=> ( ( foundationAx = $true )
=> ( ( wellorderingAx = $true )
=> ( ( descrp = $true )
=> ( ( dsetconstrI = $true )
=> ( ( dsetconstrEL = $true )
=> ( ( dsetconstrER = $true )
=> ( ( exuE1 = $true )
=> ( ( prop2setE = $true )
=> ( ( emptysetE = $true )
=> ( ( emptysetimpfalse = $true )
=> ( ( notinemptyset = $true )
=> ( ( exuE3e = $true )
=> ( ( setext = $true )
=> ( ( emptyI = $true )
=> ( ( noeltsimpempty = $true )
=> ( ( setbeta = $true )
=> ( ( nonemptyE1 = $true )
=> ( ( nonemptyI = $true )
=> ( ( nonemptyI1 = $true )
=> ( ( setadjoinIL = $true )
=> ( ( emptyinunitempty = $true )
=> ( ( setadjoinIR = $true )
=> ( ( setadjoinE = $true )
=> ( ( setadjoinOr = $true )
=> ( ( setoftrueEq = $true )
=> ( ( powersetI = $true )
=> ( ( emptyinPowerset = $true )
=> ( ( emptyInPowerset = $true )
=> ( ( powersetE = $true )
=> ( ( setunionI = $true )
=> ( ( setunionE = $true )
=> ( ( subPowSU = $true )
=> ( ( exuE2 = $true )
=> ( ( nonemptyImpWitness = $true )
=> ( ( uniqinunit = $true )
=> ( ( notinsingleton = $true )
=> ( ( eqinunit = $true )
=> ( ( singletonsswitch = $true )
=> ( ( upairsetE = $true )
=> ( ( upairsetIL = $true )
=> ( ( upairsetIR = $true )
=> ( ( emptyE1 = $true )
=> ( ( vacuousDall = $true )
=> ( ( quantDeMorgan1 = $true )
=> ( ( quantDeMorgan2 = $true )
=> ( ( quantDeMorgan3 = $true )
=> ( ( quantDeMorgan4 = $true )
=> ( ( prop2setI = $true )
=> ( ( prop2set2propI = $true )
=> ( ( notdexE = $true )
=> ( ( notdallE = $true )
=> ( ( exuI1 = $true )
=> ( ( exuI3 = $true )
=> ( ( exuI2 = $true )
=> ( ( inCongP = $true )
=> ( ( in__Cong = $true )
=> ( ( exuE3u = $true )
=> ( ( exu__Cong = $true )
=> ( ( emptyset__Cong = $true )
=> ( ( setadjoin__Cong = $true )
=> ( ( powerset__Cong = $true )
=> ( ( setunion__Cong = $true )
=> ( ( omega__Cong = $true )
=> ( ( exuEu = $true )
=> ( ( descr__Cong = $true )
=> ( ( dsetconstr__Cong = $true )
=> ( ( subsetI1 = $true )
=> ( ( eqimpsubset2 = $true )
=> ( ( eqimpsubset1 = $true )
=> ( ( subsetI2 = $true )
=> ( ( emptysetsubset = $true )
=> ( ( subsetE = $true )
=> ( ( subsetE2 = $true )
=> ( ( notsubsetI = $true )
=> ( ( notequalI1 = $true )
=> ( ( notequalI2 = $true )
=> ( ( subsetRefl = $true )
=> ( ( subsetTrans = $true )
=> ( ( setadjoinSub = $true )
=> ( ( setadjoinSub2 = $true )
=> ( ( subset2powerset = $true )
=> ( ( setextsub = $true )
=> ( ( subsetemptysetimpeq = $true )
=> ( ( powersetI1 = $true )
=> ( ( powersetE1 = $true )
=> ( ( inPowerset = $true )
=> ( ( powersetsubset = $true )
=> ( ( sepInPowerset = $true )
=> ( ( sepSubset = $true )
=> ( ( binunionIL = $true )
=> ( ( upairset2IR = $true )
=> ( ( binunionIR = $true )
=> ( ( binunionEcases = $true )
=> ( ( binunionE = $true )
=> ( ( binunionLsub = $true )
=> ( ( binunionRsub = $true )
=> ( ( binintersectI = $true )
=> ( ( binintersectSubset5 = $true )
=> ( ( binintersectEL = $true )
=> ( ( binintersectLsub = $true )
=> ( ( binintersectSubset2 = $true )
=> ( ( binintersectSubset3 = $true )
=> ( ( binintersectER = $true )
=> ( ( disjointsetsI1 = $true )
=> ( ( binintersectRsub = $true )
=> ( ( binintersectSubset4 = $true )
=> ( ( binintersectSubset1 = $true )
=> ( ( bs114d = $true )
=> ( ( setminusI = $true )
=> ( ( setminusEL = $true )
=> ( ( setminusER = $true )
=> ( ( setminusSubset2 = $true )
=> ( ( setminusERneg = $true )
=> ( ( setminusELneg = $true )
=> ( ( setminusILneg = $true )
=> ( ( setminusIRneg = $true )
=> ( ( setminusLsub = $true )
=> ( ( setminusSubset1 = $true )
=> ( ( symdiffE = $true )
=> ( ( symdiffI1 = $true )
=> ( ( symdiffI2 = $true )
=> ( ( symdiffIneg1 = $true )
=> ( ( symdiffIneg2 = $true )
=> ( ( secondinupair = $true )
=> ( ( setukpairIL = $true )
=> ( ( setukpairIR = $true )
=> ( ( kpairiskpair = $true )
=> ( ( kpairp = $true )
=> ( ( singletonsubset = $true )
=> ( ( singletoninpowerset = $true )
=> ( ( singletoninpowunion = $true )
=> ( ( upairset2E = $true )
=> ( ( upairsubunion = $true )
=> ( ( upairinpowunion = $true )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ X1 )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X2 )
= $true )
=> ( $true
= ( subset @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f251]) ).
thf(f251,plain,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X0 @ X1 )
=> ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ( subset @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f150]) ).
thf(f150,negated_conjecture,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ! [X1: $i,X3: $i,X4: $i] :
( ( in @ X1 @ X3 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( subset @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X3 @ X4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f149]) ).
thf(f149,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ! [X1: $i,X3: $i,X4: $i] :
( ( in @ X1 @ X3 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( subset @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X3 @ X4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.EC9PjZGDVh/DTF2THF_12319.p',ubforcartprodlem1) ).
thf(f9109,plain,
( ( upairsubunion != $true )
| ~ spl395_14 ),
inference(subsumption_resolution,[status(thm)],[f9108,f1467]) ).
thf(f1467,plain,
( ( in @ sK128 @ sK127 )
= $true ),
inference(cnf_transformation,[status(thm)],[f834]) ).
thf(f9108,plain,
( ( ( in @ sK128 @ sK127 )
!= $true )
| ( upairsubunion != $true )
| ~ spl395_14 ),
inference(subsumption_resolution,[status(thm)],[f9101,f1466]) ).
thf(f1466,plain,
( ( in @ sK125 @ sK126 )
= $true ),
inference(cnf_transformation,[status(thm)],[f834]) ).
thf(f9101,plain,
( ( ( in @ sK125 @ sK126 )
!= $true )
| ( ( in @ sK128 @ sK127 )
!= $true )
| ( upairsubunion != $true )
| ~ spl395_14 ),
inference(trivial_inequality_removal,[status(thm)],[f9095]) ).
thf(f9095,plain,
( ( upairsubunion != $true )
| ( ( in @ sK125 @ sK126 )
!= $true )
| ( $true != $true )
| ( ( in @ sK128 @ sK127 )
!= $true )
| ~ spl395_14 ),
inference(superposition,[status(thm)],[f9091,f1339]) ).
thf(f1339,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( subset @ ( setadjoin @ X1 @ ( setadjoin @ X3 @ emptyset ) ) @ ( binunion @ X2 @ X0 ) )
= $true )
| ( ( in @ X3 @ X0 )
!= $true )
| ( ( in @ X1 @ X2 )
!= $true )
| ( upairsubunion != $true ) ),
inference(cnf_transformation,[status(thm)],[f687]) ).
thf(f687,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ X2 )
!= $true )
| ! [X3: $i] :
( ( ( subset @ ( setadjoin @ X1 @ ( setadjoin @ X3 @ emptyset ) ) @ ( binunion @ X2 @ X0 ) )
= $true )
| ( ( in @ X3 @ X0 )
!= $true ) ) )
| ( upairsubunion != $true ) )
& ( ( upairsubunion = $true )
| ( ( $true
= ( in @ sK34 @ sK35 ) )
& ( $true
!= ( subset @ ( setadjoin @ sK34 @ ( setadjoin @ sK36 @ emptyset ) ) @ ( binunion @ sK35 @ sK33 ) ) )
& ( ( in @ sK36 @ sK33 )
= $true ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK33,sK34,sK35,sK36])],[f684,f686,f685]) ).
thf(f685,plain,
( ? [X4: $i,X5: $i,X6: $i] :
( ( ( in @ X5 @ X6 )
= $true )
& ? [X7: $i] :
( ( ( subset @ ( setadjoin @ X5 @ ( setadjoin @ X7 @ emptyset ) ) @ ( binunion @ X6 @ X4 ) )
!= $true )
& ( ( in @ X7 @ X4 )
= $true ) ) )
=> ( ( $true
= ( in @ sK34 @ sK35 ) )
& ? [X7: $i] :
( ( ( subset @ ( setadjoin @ sK34 @ ( setadjoin @ X7 @ emptyset ) ) @ ( binunion @ sK35 @ sK33 ) )
!= $true )
& ( ( in @ X7 @ sK33 )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f686,plain,
( ? [X7: $i] :
( ( ( subset @ ( setadjoin @ sK34 @ ( setadjoin @ X7 @ emptyset ) ) @ ( binunion @ sK35 @ sK33 ) )
!= $true )
& ( ( in @ X7 @ sK33 )
= $true ) )
=> ( ( $true
!= ( subset @ ( setadjoin @ sK34 @ ( setadjoin @ sK36 @ emptyset ) ) @ ( binunion @ sK35 @ sK33 ) ) )
& ( ( in @ sK36 @ sK33 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f684,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ X2 )
!= $true )
| ! [X3: $i] :
( ( ( subset @ ( setadjoin @ X1 @ ( setadjoin @ X3 @ emptyset ) ) @ ( binunion @ X2 @ X0 ) )
= $true )
| ( ( in @ X3 @ X0 )
!= $true ) ) )
| ( upairsubunion != $true ) )
& ( ( upairsubunion = $true )
| ? [X4: $i,X5: $i,X6: $i] :
( ( ( in @ X5 @ X6 )
= $true )
& ? [X7: $i] :
( ( ( subset @ ( setadjoin @ X5 @ ( setadjoin @ X7 @ emptyset ) ) @ ( binunion @ X6 @ X4 ) )
!= $true )
& ( ( in @ X7 @ X4 )
= $true ) ) ) ) ),
inference(rectify,[status(thm)],[f683]) ).
thf(f683,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ X2 )
!= $true )
| ! [X3: $i] :
( ( ( subset @ ( setadjoin @ X1 @ ( setadjoin @ X3 @ emptyset ) ) @ ( binunion @ X2 @ X0 ) )
= $true )
| ( ( in @ X3 @ X0 )
!= $true ) ) )
| ( upairsubunion != $true ) )
& ( ( upairsubunion = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ X2 )
= $true )
& ? [X3: $i] :
( ( ( subset @ ( setadjoin @ X1 @ ( setadjoin @ X3 @ emptyset ) ) @ ( binunion @ X2 @ X0 ) )
!= $true )
& ( ( in @ X3 @ X0 )
= $true ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f621]) ).
thf(f621,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ X2 )
!= $true )
| ! [X3: $i] :
( ( ( subset @ ( setadjoin @ X1 @ ( setadjoin @ X3 @ emptyset ) ) @ ( binunion @ X2 @ X0 ) )
= $true )
| ( ( in @ X3 @ X0 )
!= $true ) ) )
<=> ( upairsubunion = $true ) ),
inference(ennf_transformation,[status(thm)],[f248]) ).
thf(f248,plain,
( ( upairsubunion = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ X2 )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
=> ( ( subset @ ( setadjoin @ X1 @ ( setadjoin @ X3 @ emptyset ) ) @ ( binunion @ X2 @ X0 ) )
= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f247]) ).
thf(f247,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ X2 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( subset @ ( setadjoin @ X1 @ ( setadjoin @ X3 @ emptyset ) ) @ ( binunion @ X2 @ X0 ) ) ) )
= upairsubunion ),
inference(rectify,[status(thm)],[f147]) ).
thf(f147,axiom,
! [X4: $i,X1: $i,X3: $i] :
( ( ( in @ X1 @ X3 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( subset @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ ( binunion @ X3 @ X4 ) ) ) )
= upairsubunion ),
file('/export/starexec/sandbox/tmp/tmp.EC9PjZGDVh/DTF2THF_12319.p',upairsubunion) ).
thf(f9091,plain,
( ( $true
!= ( subset @ ( setadjoin @ sK125 @ ( setadjoin @ sK128 @ emptyset ) ) @ ( binunion @ sK126 @ sK127 ) ) )
| ~ spl395_14 ),
inference(subsumption_resolution,[status(thm)],[f9088,f1584]) ).
thf(f1584,plain,
powersetsubset = $true,
inference(cnf_transformation,[status(thm)],[f834]) ).
thf(f9088,plain,
( ( powersetsubset != $true )
| ( $true
!= ( subset @ ( setadjoin @ sK125 @ ( setadjoin @ sK128 @ emptyset ) ) @ ( binunion @ sK126 @ sK127 ) ) )
| ~ spl395_14 ),
inference(trivial_inequality_removal,[status(thm)],[f9080]) ).
thf(f9080,plain,
( ( powersetsubset != $true )
| ( $true != $true )
| ( $true
!= ( subset @ ( setadjoin @ sK125 @ ( setadjoin @ sK128 @ emptyset ) ) @ ( binunion @ sK126 @ sK127 ) ) )
| ~ spl395_14 ),
inference(superposition,[status(thm)],[f9073,f1688]) ).
thf(f1688,plain,
! [X0: $i,X1: $i] :
( ( ( subset @ ( powerset @ X0 ) @ ( powerset @ X1 ) )
= $true )
| ( powersetsubset != $true )
| ( ( subset @ X0 @ X1 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f934]) ).
thf(f934,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
!= $true )
| ( ( subset @ ( powerset @ X0 ) @ ( powerset @ X1 ) )
= $true ) )
| ( powersetsubset != $true ) )
& ( ( powersetsubset = $true )
| ( ( ( subset @ sK187 @ sK188 )
= $true )
& ( ( subset @ ( powerset @ sK187 ) @ ( powerset @ sK188 ) )
!= $true ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK187,sK188])],[f932,f933]) ).
thf(f933,plain,
( ? [X2: $i,X3: $i] :
( ( $true
= ( subset @ X2 @ X3 ) )
& ( ( subset @ ( powerset @ X2 ) @ ( powerset @ X3 ) )
!= $true ) )
=> ( ( ( subset @ sK187 @ sK188 )
= $true )
& ( ( subset @ ( powerset @ sK187 ) @ ( powerset @ sK188 ) )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f932,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
!= $true )
| ( ( subset @ ( powerset @ X0 ) @ ( powerset @ X1 ) )
= $true ) )
| ( powersetsubset != $true ) )
& ( ( powersetsubset = $true )
| ? [X2: $i,X3: $i] :
( ( $true
= ( subset @ X2 @ X3 ) )
& ( ( subset @ ( powerset @ X2 ) @ ( powerset @ X3 ) )
!= $true ) ) ) ),
inference(rectify,[status(thm)],[f931]) ).
thf(f931,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
!= $true )
| ( ( subset @ ( powerset @ X0 ) @ ( powerset @ X1 ) )
= $true ) )
| ( powersetsubset != $true ) )
& ( ( powersetsubset = $true )
| ? [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
& ( ( subset @ ( powerset @ X0 ) @ ( powerset @ X1 ) )
!= $true ) ) ) ),
inference(nnf_transformation,[status(thm)],[f583]) ).
thf(f583,plain,
( ! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
!= $true )
| ( ( subset @ ( powerset @ X0 ) @ ( powerset @ X1 ) )
= $true ) )
<=> ( powersetsubset = $true ) ),
inference(ennf_transformation,[status(thm)],[f329]) ).
thf(f329,plain,
( ( powersetsubset = $true )
<=> ! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
=> ( ( subset @ ( powerset @ X0 ) @ ( powerset @ X1 ) )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f328]) ).
thf(f328,plain,
! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
=> ( subset @ ( powerset @ X0 ) @ ( powerset @ X1 ) ) )
= powersetsubset ),
inference(rectify,[status(thm)],[f98]) ).
thf(f98,axiom,
! [X3: $i,X4: $i] :
( ( ( subset @ X3 @ X4 )
=> ( subset @ ( powerset @ X3 ) @ ( powerset @ X4 ) ) )
= powersetsubset ),
file('/export/starexec/sandbox/tmp/tmp.EC9PjZGDVh/DTF2THF_12319.p',powersetsubset) ).
thf(f9073,plain,
( ( ( subset @ ( powerset @ ( setadjoin @ sK125 @ ( setadjoin @ sK128 @ emptyset ) ) ) @ ( powerset @ ( binunion @ sK126 @ sK127 ) ) )
!= $true )
| ~ spl395_14 ),
inference(subsumption_resolution,[status(thm)],[f9007,f1499]) ).
thf(f1499,plain,
inPowerset = $true,
inference(cnf_transformation,[status(thm)],[f834]) ).
thf(f9007,plain,
( ( inPowerset != $true )
| ( ( subset @ ( powerset @ ( setadjoin @ sK125 @ ( setadjoin @ sK128 @ emptyset ) ) ) @ ( powerset @ ( binunion @ sK126 @ sK127 ) ) )
!= $true )
| ~ spl395_14 ),
inference(trivial_inequality_removal,[status(thm)],[f8973]) ).
thf(f8973,plain,
( ( $true != $true )
| ( inPowerset != $true )
| ( ( subset @ ( powerset @ ( setadjoin @ sK125 @ ( setadjoin @ sK128 @ emptyset ) ) ) @ ( powerset @ ( binunion @ sK126 @ sK127 ) ) )
!= $true )
| ~ spl395_14 ),
inference(superposition,[status(thm)],[f8939,f1771]) ).
thf(f1771,plain,
! [X1: $i] :
( ( ( in @ X1 @ ( powerset @ X1 ) )
= $true )
| ( inPowerset != $true ) ),
inference(cnf_transformation,[status(thm)],[f1025]) ).
thf(f1025,plain,
( ( ( inPowerset = $true )
| ( ( in @ sK239 @ ( powerset @ sK239 ) )
!= $true ) )
& ( ! [X1: $i] :
( ( in @ X1 @ ( powerset @ X1 ) )
= $true )
| ( inPowerset != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK239])],[f1023,f1024]) ).
thf(f1024,plain,
( ? [X0: $i] :
( ( in @ X0 @ ( powerset @ X0 ) )
!= $true )
=> ( ( in @ sK239 @ ( powerset @ sK239 ) )
!= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1023,plain,
( ( ( inPowerset = $true )
| ? [X0: $i] :
( ( in @ X0 @ ( powerset @ X0 ) )
!= $true ) )
& ( ! [X1: $i] :
( ( in @ X1 @ ( powerset @ X1 ) )
= $true )
| ( inPowerset != $true ) ) ),
inference(rectify,[status(thm)],[f1022]) ).
thf(f1022,plain,
( ( ( inPowerset = $true )
| ? [X0: $i] :
( ( in @ X0 @ ( powerset @ X0 ) )
!= $true ) )
& ( ! [X0: $i] :
( ( in @ X0 @ ( powerset @ X0 ) )
= $true )
| ( inPowerset != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f202]) ).
thf(f202,plain,
( ( inPowerset = $true )
<=> ! [X0: $i] :
( ( in @ X0 @ ( powerset @ X0 ) )
= $true ) ),
inference(fool_elimination,[status(thm)],[f201]) ).
thf(f201,plain,
! [X0: $i] :
( ( in @ X0 @ ( powerset @ X0 ) )
= inPowerset ),
inference(rectify,[status(thm)],[f97]) ).
thf(f97,axiom,
! [X3: $i] :
( ( in @ X3 @ ( powerset @ X3 ) )
= inPowerset ),
file('/export/starexec/sandbox/tmp/tmp.EC9PjZGDVh/DTF2THF_12319.p',inPowerset) ).
thf(f8939,plain,
( ! [X0: $i] :
( ( $true
!= ( in @ ( setadjoin @ sK125 @ ( setadjoin @ sK128 @ emptyset ) ) @ X0 ) )
| ( ( subset @ X0 @ ( powerset @ ( binunion @ sK126 @ sK127 ) ) )
!= $true ) )
| ~ spl395_14 ),
inference(subsumption_resolution,[status(thm)],[f8925,f1463]) ).
thf(f1463,plain,
binintersectSubset4 = $true,
inference(cnf_transformation,[status(thm)],[f834]) ).
thf(f8925,plain,
( ! [X0: $i] :
( ( ( subset @ X0 @ ( powerset @ ( binunion @ sK126 @ sK127 ) ) )
!= $true )
| ( binintersectSubset4 != $true )
| ( $true
!= ( in @ ( setadjoin @ sK125 @ ( setadjoin @ sK128 @ emptyset ) ) @ X0 ) ) )
| ~ spl395_14 ),
inference(superposition,[status(thm)],[f8592,f1841]) ).
thf(f1841,plain,
! [X2: $i,X3: $i] :
( ( ( binintersect @ X2 @ X3 )
= X3 )
| ( binintersectSubset4 != $true )
| ( ( subset @ X3 @ X2 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f1111]) ).
thf(f1111,plain,
( ( ( binintersectSubset4 = $true )
| ( ( sK288
!= ( binintersect @ sK287 @ sK288 ) )
& ( ( subset @ sK288 @ sK287 )
= $true ) ) )
& ( ! [X2: $i,X3: $i] :
( ( ( binintersect @ X2 @ X3 )
= X3 )
| ( ( subset @ X3 @ X2 )
!= $true ) )
| ( binintersectSubset4 != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK287,sK288])],[f1109,f1110]) ).
thf(f1110,plain,
( ? [X0: $i,X1: $i] :
( ( ( binintersect @ X0 @ X1 )
!= X1 )
& ( ( subset @ X1 @ X0 )
= $true ) )
=> ( ( sK288
!= ( binintersect @ sK287 @ sK288 ) )
& ( ( subset @ sK288 @ sK287 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1109,plain,
( ( ( binintersectSubset4 = $true )
| ? [X0: $i,X1: $i] :
( ( ( binintersect @ X0 @ X1 )
!= X1 )
& ( ( subset @ X1 @ X0 )
= $true ) ) )
& ( ! [X2: $i,X3: $i] :
( ( ( binintersect @ X2 @ X3 )
= X3 )
| ( ( subset @ X3 @ X2 )
!= $true ) )
| ( binintersectSubset4 != $true ) ) ),
inference(rectify,[status(thm)],[f1108]) ).
thf(f1108,plain,
( ( ( binintersectSubset4 = $true )
| ? [X0: $i,X1: $i] :
( ( ( binintersect @ X0 @ X1 )
!= X1 )
& ( ( subset @ X1 @ X0 )
= $true ) ) )
& ( ! [X0: $i,X1: $i] :
( ( ( binintersect @ X0 @ X1 )
= X1 )
| ( ( subset @ X1 @ X0 )
!= $true ) )
| ( binintersectSubset4 != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f502]) ).
thf(f502,plain,
( ( binintersectSubset4 = $true )
<=> ! [X0: $i,X1: $i] :
( ( ( binintersect @ X0 @ X1 )
= X1 )
| ( ( subset @ X1 @ X0 )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f220]) ).
thf(f220,plain,
( ! [X0: $i,X1: $i] :
( ( ( subset @ X1 @ X0 )
= $true )
=> ( ( binintersect @ X0 @ X1 )
= X1 ) )
<=> ( binintersectSubset4 = $true ) ),
inference(fool_elimination,[status(thm)],[f219]) ).
thf(f219,plain,
( binintersectSubset4
= ( ! [X0: $i,X1: $i] :
( ( subset @ X1 @ X0 )
=> ( ( binintersect @ X0 @ X1 )
= X1 ) ) ) ),
inference(rectify,[status(thm)],[f117]) ).
thf(f117,axiom,
( binintersectSubset4
= ( ! [X3: $i,X4: $i] :
( ( subset @ X4 @ X3 )
=> ( ( binintersect @ X3 @ X4 )
= X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.EC9PjZGDVh/DTF2THF_12319.p',binintersectSubset4) ).
thf(f8592,plain,
( ! [X1: $i] :
( ( in @ ( setadjoin @ sK125 @ ( setadjoin @ sK128 @ emptyset ) ) @ ( binintersect @ ( powerset @ ( binunion @ sK126 @ sK127 ) ) @ X1 ) )
!= $true )
| ~ spl395_14 ),
inference(avatar_component_clause,[status(thm)],[f8591]) ).
thf(f8591,definition,
( spl395_14
<=> ! [X1: $i] :
( ( in @ ( setadjoin @ sK125 @ ( setadjoin @ sK128 @ emptyset ) ) @ ( binintersect @ ( powerset @ ( binunion @ sK126 @ sK127 ) ) @ X1 ) )
!= $true ) ),
introduced(definition,[new_symbols(naming,[spl395_14])],[avatar_definition]) ).
thf(f8880,plain,
~ spl395_13,
inference(avatar_contradiction_clause,[status(thm)],[f8879]) ).
thf(f8879,plain,
( $false
| ~ spl395_13 ),
inference(subsumption_resolution,[status(thm)],[f8878,f1466]) ).
thf(f8878,plain,
( ( ( in @ sK125 @ sK126 )
!= $true )
| ~ spl395_13 ),
inference(subsumption_resolution,[status(thm)],[f8870,f1535]) ).
thf(f1535,plain,
singletoninpowunion = $true,
inference(cnf_transformation,[status(thm)],[f834]) ).
thf(f8870,plain,
( ( singletoninpowunion != $true )
| ( ( in @ sK125 @ sK126 )
!= $true )
| ~ spl395_13 ),
inference(trivial_inequality_removal,[status(thm)],[f8858]) ).
thf(f8858,plain,
( ( $true != $true )
| ( ( in @ sK125 @ sK126 )
!= $true )
| ( singletoninpowunion != $true )
| ~ spl395_13 ),
inference(superposition,[status(thm)],[f8650,f1838]) ).
thf(f1838,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ ( setadjoin @ X5 @ emptyset ) @ ( powerset @ ( binunion @ X4 @ X3 ) ) )
= $true )
| ( singletoninpowunion != $true )
| ( ( in @ X5 @ X4 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f1107]) ).
thf(f1107,plain,
( ( ( singletoninpowunion = $true )
| ( ( ( in @ ( setadjoin @ sK286 @ emptyset ) @ ( powerset @ ( binunion @ sK285 @ sK284 ) ) )
!= $true )
& ( ( in @ sK286 @ sK285 )
= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ ( setadjoin @ X5 @ emptyset ) @ ( powerset @ ( binunion @ X4 @ X3 ) ) )
= $true )
| ( ( in @ X5 @ X4 )
!= $true ) )
| ( singletoninpowunion != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK284,sK285,sK286])],[f1105,f1106]) ).
thf(f1106,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X0 ) ) )
!= $true )
& ( ( in @ X2 @ X1 )
= $true ) )
=> ( ( ( in @ ( setadjoin @ sK286 @ emptyset ) @ ( powerset @ ( binunion @ sK285 @ sK284 ) ) )
!= $true )
& ( ( in @ sK286 @ sK285 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1105,plain,
( ( ( singletoninpowunion = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X0 ) ) )
!= $true )
& ( ( in @ X2 @ X1 )
= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ ( setadjoin @ X5 @ emptyset ) @ ( powerset @ ( binunion @ X4 @ X3 ) ) )
= $true )
| ( ( in @ X5 @ X4 )
!= $true ) )
| ( singletoninpowunion != $true ) ) ),
inference(rectify,[status(thm)],[f1104]) ).
thf(f1104,plain,
( ( ( singletoninpowunion = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X0 ) ) )
!= $true )
& ( ( in @ X2 @ X1 )
= $true ) ) )
& ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X0 ) ) )
= $true )
| ( ( in @ X2 @ X1 )
!= $true ) )
| ( singletoninpowunion != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f578]) ).
thf(f578,plain,
( ( singletoninpowunion = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X0 ) ) )
= $true )
| ( ( in @ X2 @ X1 )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f269]) ).
thf(f269,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
=> ( ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X0 ) ) )
= $true ) )
<=> ( singletoninpowunion = $true ) ),
inference(fool_elimination,[status(thm)],[f268]) ).
thf(f268,plain,
( singletoninpowunion
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ X1 )
=> ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X0 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f145]) ).
thf(f145,axiom,
( singletoninpowunion
= ( ! [X4: $i,X3: $i,X1: $i] :
( ( in @ X1 @ X3 )
=> ( in @ ( setadjoin @ X1 @ emptyset ) @ ( powerset @ ( binunion @ X3 @ X4 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.EC9PjZGDVh/DTF2THF_12319.p',singletoninpowunion) ).
thf(f8650,plain,
( ( ( in @ ( setadjoin @ sK125 @ emptyset ) @ ( powerset @ ( binunion @ sK126 @ sK127 ) ) )
!= $true )
| ~ spl395_13 ),
inference(subsumption_resolution,[status(thm)],[f8640,f1542]) ).
thf(f1542,plain,
eqimpsubset2 = $true,
inference(cnf_transformation,[status(thm)],[f834]) ).
thf(f8640,plain,
( ( eqimpsubset2 != $true )
| ( ( in @ ( setadjoin @ sK125 @ emptyset ) @ ( powerset @ ( binunion @ sK126 @ sK127 ) ) )
!= $true )
| ~ spl395_13 ),
inference(trivial_inequality_removal,[status(thm)],[f8615]) ).
thf(f8615,plain,
( ( $true != $true )
| ( ( in @ ( setadjoin @ sK125 @ emptyset ) @ ( powerset @ ( binunion @ sK126 @ sK127 ) ) )
!= $true )
| ( eqimpsubset2 != $true )
| ~ spl395_13 ),
inference(superposition,[status(thm)],[f8609,f2011]) ).
thf(f2011,plain,
! [X3: $i] :
( ( ( subset @ X3 @ X3 )
= $true )
| ( eqimpsubset2 != $true ) ),
inference(equality_resolution,[status(thm)],[f1701]) ).
thf(f1701,plain,
! [X2: $i,X3: $i] :
( ( X2 != X3 )
| ( $true
= ( subset @ X2 @ X3 ) )
| ( eqimpsubset2 != $true ) ),
inference(cnf_transformation,[status(thm)],[f954]) ).
thf(f954,plain,
( ( ( eqimpsubset2 = $true )
| ( ( sK200 = sK199 )
& ( ( subset @ sK199 @ sK200 )
!= $true ) ) )
& ( ! [X2: $i,X3: $i] :
( ( X2 != X3 )
| ( $true
= ( subset @ X2 @ X3 ) ) )
| ( eqimpsubset2 != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK199,sK200])],[f952,f953]) ).
thf(f953,plain,
( ? [X0: $i,X1: $i] :
( ( X0 = X1 )
& ( ( subset @ X0 @ X1 )
!= $true ) )
=> ( ( sK200 = sK199 )
& ( ( subset @ sK199 @ sK200 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f952,plain,
( ( ( eqimpsubset2 = $true )
| ? [X0: $i,X1: $i] :
( ( X0 = X1 )
& ( ( subset @ X0 @ X1 )
!= $true ) ) )
& ( ! [X2: $i,X3: $i] :
( ( X2 != X3 )
| ( $true
= ( subset @ X2 @ X3 ) ) )
| ( eqimpsubset2 != $true ) ) ),
inference(rectify,[status(thm)],[f951]) ).
thf(f951,plain,
( ( ( eqimpsubset2 = $true )
| ? [X0: $i,X1: $i] :
( ( X0 = X1 )
& ( ( subset @ X0 @ X1 )
!= $true ) ) )
& ( ! [X0: $i,X1: $i] :
( ( X0 != X1 )
| ( ( subset @ X0 @ X1 )
= $true ) )
| ( eqimpsubset2 != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f512]) ).
thf(f512,plain,
( ( eqimpsubset2 = $true )
<=> ! [X0: $i,X1: $i] :
( ( X0 != X1 )
| ( ( subset @ X0 @ X1 )
= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f385]) ).
thf(f385,plain,
( ( eqimpsubset2 = $true )
<=> ! [X0: $i,X1: $i] :
( ( X0 = X1 )
=> ( ( subset @ X0 @ X1 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f384]) ).
thf(f384,plain,
( eqimpsubset2
= ( ! [X0: $i,X1: $i] :
( ( X0 = X1 )
=> ( subset @ X0 @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f79]) ).
thf(f79,axiom,
( eqimpsubset2
= ( ! [X4: $i,X3: $i] :
( ( X3 = X4 )
=> ( subset @ X4 @ X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.EC9PjZGDVh/DTF2THF_12319.p',eqimpsubset2) ).
thf(f8609,plain,
( ! [X0: $i] :
( ( ( subset @ X0 @ ( powerset @ ( binunion @ sK126 @ sK127 ) ) )
!= $true )
| ( $true
!= ( in @ ( setadjoin @ sK125 @ emptyset ) @ X0 ) ) )
| ~ spl395_13 ),
inference(subsumption_resolution,[status(thm)],[f8594,f1463]) ).
thf(f8594,plain,
( ! [X0: $i] :
( ( binintersectSubset4 != $true )
| ( $true
!= ( in @ ( setadjoin @ sK125 @ emptyset ) @ X0 ) )
| ( ( subset @ X0 @ ( powerset @ ( binunion @ sK126 @ sK127 ) ) )
!= $true ) )
| ~ spl395_13 ),
inference(superposition,[status(thm)],[f8589,f1841]) ).
thf(f8589,plain,
( ! [X0: $i] :
( ( in @ ( setadjoin @ sK125 @ emptyset ) @ ( binintersect @ ( powerset @ ( binunion @ sK126 @ sK127 ) ) @ X0 ) )
!= $true )
| ~ spl395_13 ),
inference(avatar_component_clause,[status(thm)],[f8588]) ).
thf(f8588,definition,
( spl395_13
<=> ! [X0: $i] :
( ( in @ ( setadjoin @ sK125 @ emptyset ) @ ( binintersect @ ( powerset @ ( binunion @ sK126 @ sK127 ) ) @ X0 ) )
!= $true ) ),
introduced(definition,[new_symbols(naming,[spl395_13])],[avatar_definition]) ).
thf(f8593,plain,
( spl395_13
| spl395_14 ),
inference(avatar_split_clause,[status(thm)],[f8584,f8591,f8588]) ).
thf(f8584,plain,
! [X0: $i,X1: $i] :
( ( ( in @ ( setadjoin @ sK125 @ ( setadjoin @ sK128 @ emptyset ) ) @ ( binintersect @ ( powerset @ ( binunion @ sK126 @ sK127 ) ) @ X1 ) )
!= $true )
| ( ( in @ ( setadjoin @ sK125 @ emptyset ) @ ( binintersect @ ( powerset @ ( binunion @ sK126 @ sK127 ) ) @ X0 ) )
!= $true ) ),
inference(subsumption_resolution,[status(thm)],[f8581,f1511]) ).
thf(f1511,plain,
binintersectLsub = $true,
inference(cnf_transformation,[status(thm)],[f834]) ).
thf(f8581,plain,
! [X0: $i,X1: $i] :
( ( ( in @ ( setadjoin @ sK125 @ emptyset ) @ ( binintersect @ ( powerset @ ( binunion @ sK126 @ sK127 ) ) @ X0 ) )
!= $true )
| ( ( in @ ( setadjoin @ sK125 @ ( setadjoin @ sK128 @ emptyset ) ) @ ( binintersect @ ( powerset @ ( binunion @ sK126 @ sK127 ) ) @ X1 ) )
!= $true )
| ( binintersectLsub != $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f8572]) ).
thf(f8572,plain,
! [X0: $i,X1: $i] :
( ( binintersectLsub != $true )
| ( $true != $true )
| ( ( in @ ( setadjoin @ sK125 @ emptyset ) @ ( binintersect @ ( powerset @ ( binunion @ sK126 @ sK127 ) ) @ X0 ) )
!= $true )
| ( ( in @ ( setadjoin @ sK125 @ ( setadjoin @ sK128 @ emptyset ) ) @ ( binintersect @ ( powerset @ ( binunion @ sK126 @ sK127 ) ) @ X1 ) )
!= $true ) ),
inference(superposition,[status(thm)],[f2243,f1360]) ).
thf(f1360,plain,
! [X2: $i,X3: $i] :
( ( ( subset @ ( binintersect @ X2 @ X3 ) @ X2 )
= $true )
| ( binintersectLsub != $true ) ),
inference(cnf_transformation,[status(thm)],[f714]) ).
thf(f714,plain,
( ( ( binintersectLsub = $true )
| ( ( subset @ ( binintersect @ sK52 @ sK53 ) @ sK52 )
!= $true ) )
& ( ! [X2: $i,X3: $i] :
( ( subset @ ( binintersect @ X2 @ X3 ) @ X2 )
= $true )
| ( binintersectLsub != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK52,sK53])],[f712,f713]) ).
thf(f713,plain,
( ? [X0: $i,X1: $i] :
( ( subset @ ( binintersect @ X0 @ X1 ) @ X0 )
!= $true )
=> ( ( subset @ ( binintersect @ sK52 @ sK53 ) @ sK52 )
!= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f712,plain,
( ( ( binintersectLsub = $true )
| ? [X0: $i,X1: $i] :
( ( subset @ ( binintersect @ X0 @ X1 ) @ X0 )
!= $true ) )
& ( ! [X2: $i,X3: $i] :
( ( subset @ ( binintersect @ X2 @ X3 ) @ X2 )
= $true )
| ( binintersectLsub != $true ) ) ),
inference(rectify,[status(thm)],[f711]) ).
thf(f711,plain,
( ( ( binintersectLsub = $true )
| ? [X0: $i,X1: $i] :
( ( subset @ ( binintersect @ X0 @ X1 ) @ X0 )
!= $true ) )
& ( ! [X0: $i,X1: $i] :
( ( subset @ ( binintersect @ X0 @ X1 ) @ X0 )
= $true )
| ( binintersectLsub != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f323]) ).
thf(f323,plain,
( ( binintersectLsub = $true )
<=> ! [X0: $i,X1: $i] :
( ( subset @ ( binintersect @ X0 @ X1 ) @ X0 )
= $true ) ),
inference(fool_elimination,[status(thm)],[f322]) ).
thf(f322,plain,
! [X0: $i,X1: $i] :
( ( subset @ ( binintersect @ X0 @ X1 ) @ X0 )
= binintersectLsub ),
inference(rectify,[status(thm)],[f111]) ).
thf(f111,axiom,
! [X3: $i,X4: $i] :
( ( subset @ ( binintersect @ X3 @ X4 ) @ X3 )
= binintersectLsub ),
file('/export/starexec/sandbox/tmp/tmp.EC9PjZGDVh/DTF2THF_12319.p',binintersectLsub) ).
thf(f2243,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( subset @ ( binintersect @ X0 @ ( binunion @ X1 @ X2 ) ) @ ( powerset @ ( binunion @ sK126 @ sK127 ) ) )
!= $true )
| ( ( in @ ( setadjoin @ sK125 @ ( setadjoin @ sK128 @ emptyset ) ) @ ( binintersect @ X0 @ X2 ) )
!= $true )
| ( ( in @ ( setadjoin @ sK125 @ emptyset ) @ ( binintersect @ X0 @ X1 ) )
!= $true ) ),
inference(subsumption_resolution,[status(thm)],[f2230,f1493]) ).
thf(f1493,plain,
bs114d = $true,
inference(cnf_transformation,[status(thm)],[f834]) ).
thf(f2230,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ ( setadjoin @ sK125 @ ( setadjoin @ sK128 @ emptyset ) ) @ ( binintersect @ X0 @ X2 ) )
!= $true )
| ( bs114d != $true )
| ( ( in @ ( setadjoin @ sK125 @ emptyset ) @ ( binintersect @ X0 @ X1 ) )
!= $true )
| ( ( subset @ ( binintersect @ X0 @ ( binunion @ X1 @ X2 ) ) @ ( powerset @ ( binunion @ sK126 @ sK127 ) ) )
!= $true ) ),
inference(superposition,[status(thm)],[f2174,f1609]) ).
thf(f1609,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( binunion @ ( binintersect @ X3 @ X5 ) @ ( binintersect @ X3 @ X4 ) )
= ( binintersect @ X3 @ ( binunion @ X5 @ X4 ) ) )
| ( bs114d != $true ) ),
inference(cnf_transformation,[status(thm)],[f838]) ).
thf(f838,plain,
( ( ( bs114d = $true )
| ( ( binintersect @ sK129 @ ( binunion @ sK131 @ sK130 ) )
!= ( binunion @ ( binintersect @ sK129 @ sK131 ) @ ( binintersect @ sK129 @ sK130 ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( binunion @ ( binintersect @ X3 @ X5 ) @ ( binintersect @ X3 @ X4 ) )
= ( binintersect @ X3 @ ( binunion @ X5 @ X4 ) ) )
| ( bs114d != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK129,sK130,sK131])],[f836,f837]) ).
thf(f837,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( binintersect @ X0 @ ( binunion @ X2 @ X1 ) )
!= ( binunion @ ( binintersect @ X0 @ X2 ) @ ( binintersect @ X0 @ X1 ) ) )
=> ( ( binintersect @ sK129 @ ( binunion @ sK131 @ sK130 ) )
!= ( binunion @ ( binintersect @ sK129 @ sK131 ) @ ( binintersect @ sK129 @ sK130 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f836,plain,
( ( ( bs114d = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( binintersect @ X0 @ ( binunion @ X2 @ X1 ) )
!= ( binunion @ ( binintersect @ X0 @ X2 ) @ ( binintersect @ X0 @ X1 ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( binunion @ ( binintersect @ X3 @ X5 ) @ ( binintersect @ X3 @ X4 ) )
= ( binintersect @ X3 @ ( binunion @ X5 @ X4 ) ) )
| ( bs114d != $true ) ) ),
inference(rectify,[status(thm)],[f835]) ).
thf(f835,plain,
( ( ( bs114d = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( binintersect @ X0 @ ( binunion @ X2 @ X1 ) )
!= ( binunion @ ( binintersect @ X0 @ X2 ) @ ( binintersect @ X0 @ X1 ) ) ) )
& ( ! [X0: $i,X1: $i,X2: $i] :
( ( binintersect @ X0 @ ( binunion @ X2 @ X1 ) )
= ( binunion @ ( binintersect @ X0 @ X2 ) @ ( binintersect @ X0 @ X1 ) ) )
| ( bs114d != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f433]) ).
thf(f433,plain,
( ( bs114d = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( binintersect @ X0 @ ( binunion @ X2 @ X1 ) )
= ( binunion @ ( binintersect @ X0 @ X2 ) @ ( binintersect @ X0 @ X1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f432]) ).
thf(f432,plain,
( bs114d
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( binintersect @ X0 @ ( binunion @ X2 @ X1 ) )
= ( binunion @ ( binintersect @ X0 @ X2 ) @ ( binintersect @ X0 @ X1 ) ) ) ) ),
inference(rectify,[status(thm)],[f119]) ).
thf(f119,axiom,
( bs114d
= ( ! [X3: $i,X5: $i,X4: $i] :
( ( binintersect @ X3 @ ( binunion @ X4 @ X5 ) )
= ( binunion @ ( binintersect @ X3 @ X4 ) @ ( binintersect @ X3 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.EC9PjZGDVh/DTF2THF_12319.p',bs114d) ).
thf(f2174,plain,
! [X0: $i,X1: $i] :
( ( ( subset @ ( binunion @ X0 @ X1 ) @ ( powerset @ ( binunion @ sK126 @ sK127 ) ) )
!= $true )
| ( $true
!= ( in @ ( setadjoin @ sK125 @ emptyset ) @ X0 ) )
| ( ( in @ ( setadjoin @ sK125 @ ( setadjoin @ sK128 @ emptyset ) ) @ X1 )
!= $true ) ),
inference(subsumption_resolution,[status(thm)],[f2145,f1566]) ).
thf(f2145,plain,
! [X0: $i,X1: $i] :
( ( ( in @ ( setadjoin @ sK125 @ ( setadjoin @ sK128 @ emptyset ) ) @ X1 )
!= $true )
| ( $true
!= ( in @ ( setadjoin @ sK125 @ emptyset ) @ X0 ) )
| ( ( subset @ ( binunion @ X0 @ X1 ) @ ( powerset @ ( binunion @ sK126 @ sK127 ) ) )
!= $true )
| ( upairsubunion != $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f2111]) ).
thf(f2111,plain,
! [X0: $i,X1: $i] :
( ( ( in @ ( setadjoin @ sK125 @ ( setadjoin @ sK128 @ emptyset ) ) @ X1 )
!= $true )
| ( upairsubunion != $true )
| ( $true
!= ( in @ ( setadjoin @ sK125 @ emptyset ) @ X0 ) )
| ( $true != $true )
| ( ( subset @ ( binunion @ X0 @ X1 ) @ ( powerset @ ( binunion @ sK126 @ sK127 ) ) )
!= $true ) ),
inference(superposition,[status(thm)],[f2107,f1339]) ).
thf(f2107,plain,
! [X0: $i] :
( ( ( subset @ ( setadjoin @ ( setadjoin @ sK125 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK125 @ ( setadjoin @ sK128 @ emptyset ) ) @ emptyset ) ) @ X0 )
!= $true )
| ( ( subset @ X0 @ ( powerset @ ( binunion @ sK126 @ sK127 ) ) )
!= $true ) ),
inference(subsumption_resolution,[status(thm)],[f2102,f1564]) ).
thf(f1564,plain,
subsetTrans = $true,
inference(cnf_transformation,[status(thm)],[f834]) ).
thf(f2102,plain,
! [X0: $i] :
( ( ( subset @ ( setadjoin @ ( setadjoin @ sK125 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK125 @ ( setadjoin @ sK128 @ emptyset ) ) @ emptyset ) ) @ X0 )
!= $true )
| ( ( subset @ X0 @ ( powerset @ ( binunion @ sK126 @ sK127 ) ) )
!= $true )
| ( subsetTrans != $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f2098]) ).
thf(f2098,plain,
! [X0: $i] :
( ( ( subset @ ( setadjoin @ ( setadjoin @ sK125 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK125 @ ( setadjoin @ sK128 @ emptyset ) ) @ emptyset ) ) @ X0 )
!= $true )
| ( $true != $true )
| ( ( subset @ X0 @ ( powerset @ ( binunion @ sK126 @ sK127 ) ) )
!= $true )
| ( subsetTrans != $true ) ),
inference(superposition,[status(thm)],[f1468,f1658]) ).
thf(f1658,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( subset @ X1 @ X0 )
= $true )
| ( $true
!= ( subset @ X1 @ X2 ) )
| ( subsetTrans != $true )
| ( ( subset @ X2 @ X0 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f896]) ).
thf(f896,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X2 @ X0 )
!= $true )
| ( $true
!= ( subset @ X1 @ X2 ) )
| ( ( subset @ X1 @ X0 )
= $true ) )
| ( subsetTrans != $true ) )
& ( ( subsetTrans = $true )
| ( ( $true
= ( subset @ sK167 @ sK165 ) )
& ( ( subset @ sK166 @ sK167 )
= $true )
& ( ( subset @ sK166 @ sK165 )
!= $true ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK165,sK166,sK167])],[f894,f895]) ).
thf(f895,plain,
( ? [X3: $i,X4: $i,X5: $i] :
( ( ( subset @ X5 @ X3 )
= $true )
& ( ( subset @ X4 @ X5 )
= $true )
& ( ( subset @ X4 @ X3 )
!= $true ) )
=> ( ( $true
= ( subset @ sK167 @ sK165 ) )
& ( ( subset @ sK166 @ sK167 )
= $true )
& ( ( subset @ sK166 @ sK165 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f894,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X2 @ X0 )
!= $true )
| ( $true
!= ( subset @ X1 @ X2 ) )
| ( ( subset @ X1 @ X0 )
= $true ) )
| ( subsetTrans != $true ) )
& ( ( subsetTrans = $true )
| ? [X3: $i,X4: $i,X5: $i] :
( ( ( subset @ X5 @ X3 )
= $true )
& ( ( subset @ X4 @ X5 )
= $true )
& ( ( subset @ X4 @ X3 )
!= $true ) ) ) ),
inference(rectify,[status(thm)],[f893]) ).
thf(f893,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X2 @ X0 )
!= $true )
| ( $true
!= ( subset @ X1 @ X2 ) )
| ( ( subset @ X1 @ X0 )
= $true ) )
| ( subsetTrans != $true ) )
& ( ( subsetTrans = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X2 @ X0 )
= $true )
& ( $true
= ( subset @ X1 @ X2 ) )
& ( ( subset @ X1 @ X0 )
!= $true ) ) ) ),
inference(nnf_transformation,[status(thm)],[f531]) ).
thf(f531,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X2 @ X0 )
!= $true )
| ( $true
!= ( subset @ X1 @ X2 ) )
| ( ( subset @ X1 @ X0 )
= $true ) )
<=> ( subsetTrans = $true ) ),
inference(flattening,[status(thm)],[f530]) ).
thf(f530,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X1 @ X0 )
= $true )
| ( ( subset @ X2 @ X0 )
!= $true )
| ( $true
!= ( subset @ X1 @ X2 ) ) )
<=> ( subsetTrans = $true ) ),
inference(ennf_transformation,[status(thm)],[f184]) ).
thf(f184,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( subset @ X1 @ X2 ) )
=> ( ( ( subset @ X2 @ X0 )
= $true )
=> ( ( subset @ X1 @ X0 )
= $true ) ) )
<=> ( subsetTrans = $true ) ),
inference(fool_elimination,[status(thm)],[f183]) ).
thf(f183,plain,
( subsetTrans
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( subset @ X1 @ X2 )
=> ( ( subset @ X2 @ X0 )
=> ( subset @ X1 @ X0 ) ) ) ) ),
inference(rectify,[status(thm)],[f89]) ).
thf(f89,axiom,
( subsetTrans
= ( ! [X5: $i,X3: $i,X4: $i] :
( ( subset @ X3 @ X4 )
=> ( ( subset @ X4 @ X5 )
=> ( subset @ X3 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.EC9PjZGDVh/DTF2THF_12319.p',subsetTrans) ).
thf(f1468,plain,
( $true
!= ( subset @ ( setadjoin @ ( setadjoin @ sK125 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK125 @ ( setadjoin @ sK128 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ sK126 @ sK127 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f834]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU627^1 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.33 % Computer : n028.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue Feb 24 12:28:57 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.29/0.45 ---- Original DTF file ---
% 0.29/0.46 thf(spec,logic,$$dhol).
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 % File : SEU627^1 : TPTP v9.2.1. Released v3.7.0.
% 0.29/0.46 % Domain : Set Theory
% 0.29/0.46 % Problem : Ordered Pairs - Cartesian Products
% 0.29/0.46 % Version : Especial.
% 0.29/0.46 % English : (! A:i.! B:i.! x:i.in x A -> (! y:i.in y B -> subset (setadjoin
% 0.29/0.46 % (setadjoin x emptyset) (setadjoin (setadjoin x
% 0.29/0.46 % (setadjoin y emptyset)) emptyset)) (powerset (binunion A B))))
% 0.29/0.46
% 0.29/0.46 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.29/0.46 % Source : [Bro08]
% 0.29/0.46 % Names : ZFC129g [Bro08]
% 0.29/0.46
% 0.29/0.46 % Status : Theorem
% 0.29/0.46 % Rating : 0.67 v9.1.0, 0.62 v9.0.0, 0.70 v8.2.0, 0.77 v8.1.0, 0.73 v7.5.0, 0.71 v7.4.0, 0.56 v7.3.0, 0.67 v7.2.0, 0.62 v7.1.0, 0.75 v7.0.0, 0.71 v6.4.0, 0.83 v6.3.0, 0.80 v6.2.0, 1.00 v5.4.0, 0.80 v5.2.0, 1.00 v5.0.0, 0.80 v4.1.0, 1.00 v3.7.0
% 0.29/0.46 % Syntax : Number of formulae : 315 ( 148 unt; 166 typ; 148 def)
% 0.29/0.46 % Number of atoms : 782 ( 209 equ; 0 cnn)
% 0.29/0.46 % Maximal formula atoms : 146 ( 5 avg)
% 0.29/0.46 % Number of connectives : 1334 ( 47 ~; 7 |; 32 &; 891 @)
% 0.29/0.46 % ( 14 <=>; 343 =>; 0 <=; 0 <~>)
% 0.29/0.46 % Maximal formula depth : 158 ( 2 avg)
% 0.29/0.46 % Number of types : 2 ( 0 usr)
% 0.29/0.46 % Number of type conns : 69 ( 69 >; 0 *; 0 +; 0 <<)
% 0.29/0.46 % Number of symbols : 169 ( 166 usr; 147 con; 0-2 aty)
% 0.29/0.46 % Number of variables : 428 ( 36 ^; 359 !; 33 ?; 428 :)
% 0.29/0.46 % SPC : TH0_THM_EQU_NAR
% 0.29/0.46
% 0.29/0.46 % Comments : http://mathgate.info/detsetitem.php?id=184
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 thf(in_type,type,
% 0.29/0.46 in: $i > $i > $o ).
% 0.29/0.46
% 0.29/0.46 thf(exu_type,type,
% 0.29/0.46 exu: ( $i > $o ) > $o ).
% 0.29/0.46
% 0.29/0.46 thf(exu,definition,
% 0.29/0.46 ( exu
% 0.29/0.46 = ( ^ [Xphi: $i > $o] :
% 0.29/0.46 ? [Xx: $i] :
% 0.29/0.46 ( ( Xphi @ Xx )
% 0.29/0.46 & ! [Xy: $i] :
% 0.29/0.46 ( ( Xphi @ Xy )
% 0.29/0.46 => ( Xx = Xy ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setextAx_type,type,
% 0.29/0.46 setextAx: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setextAx,definition,
% 0.29/0.46 ( setextAx
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 <=> ( in @ Xx @ B ) )
% 0.29/0.46 => ( A = B ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(emptyset_type,type,
% 0.29/0.46 emptyset: $i ).
% 0.29/0.46
% 0.29/0.46 thf(emptysetAx_type,type,
% 0.29/0.46 emptysetAx: $o ).
% 0.29/0.46
% 0.29/0.46 thf(emptysetAx,definition,
% 0.29/0.46 ( emptysetAx
% 0.29/0.46 = ( ! [Xx: $i] :
% 0.29/0.46 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoin_type,type,
% 0.29/0.46 setadjoin: $i > $i > $i ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoinAx_type,type,
% 0.29/0.46 setadjoinAx: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoinAx,definition,
% 0.29/0.46 ( setadjoinAx
% 0.29/0.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.29/0.46 <=> ( ( Xy = Xx )
% 0.29/0.46 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(powerset_type,type,
% 0.29/0.46 powerset: $i > $i ).
% 0.29/0.46
% 0.29/0.46 thf(powersetAx_type,type,
% 0.29/0.46 powersetAx: $o ).
% 0.29/0.46
% 0.29/0.46 thf(powersetAx,definition,
% 0.29/0.46 ( powersetAx
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( in @ B @ ( powerset @ A ) )
% 0.29/0.46 <=> ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ B )
% 0.29/0.46 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setunion_type,type,
% 0.29/0.46 setunion: $i > $i ).
% 0.29/0.46
% 0.29/0.46 thf(setunionAx_type,type,
% 0.29/0.46 setunionAx: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setunionAx,definition,
% 0.29/0.46 ( setunionAx
% 0.29/0.46 = ( ! [A: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ ( setunion @ A ) )
% 0.29/0.46 <=> ? [B: $i] :
% 0.29/0.46 ( ( in @ Xx @ B )
% 0.29/0.46 & ( in @ B @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(omega_type,type,
% 0.29/0.46 omega: $i ).
% 0.29/0.46
% 0.29/0.46 thf(omega0Ax_type,type,
% 0.29/0.46 omega0Ax: $o ).
% 0.29/0.46
% 0.29/0.46 thf(omega0Ax,definition,
% 0.29/0.46 ( omega0Ax
% 0.29/0.46 = ( in @ emptyset @ omega ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(omegaSAx_type,type,
% 0.29/0.46 omegaSAx: $o ).
% 0.29/0.46
% 0.29/0.46 thf(omegaSAx,definition,
% 0.29/0.46 ( omegaSAx
% 0.29/0.46 = ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ omega )
% 0.29/0.46 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(omegaIndAx_type,type,
% 0.29/0.46 omegaIndAx: $o ).
% 0.29/0.46
% 0.29/0.46 thf(omegaIndAx,definition,
% 0.29/0.46 ( omegaIndAx
% 0.29/0.46 = ( ! [A: $i] :
% 0.29/0.46 ( ( ( in @ emptyset @ A )
% 0.29/0.46 & ! [Xx: $i] :
% 0.29/0.46 ( ( ( in @ Xx @ omega )
% 0.29/0.46 & ( in @ Xx @ A ) )
% 0.29/0.46 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ omega )
% 0.29/0.46 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(replAx_type,type,
% 0.29/0.46 replAx: $o ).
% 0.29/0.46
% 0.29/0.46 thf(replAx,definition,
% 0.29/0.46 ( replAx
% 0.29/0.46 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 0.29/0.46 ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( exu
% 0.29/0.46 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 0.29/0.46 => ? [B: $i] :
% 0.29/0.46 ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ B )
% 0.29/0.46 <=> ? [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ A )
% 0.29/0.46 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(foundationAx_type,type,
% 0.29/0.46 foundationAx: $o ).
% 0.29/0.46
% 0.29/0.46 thf(foundationAx,definition,
% 0.29/0.46 ( foundationAx
% 0.29/0.46 = ( ! [A: $i] :
% 0.29/0.46 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.29/0.46 => ? [B: $i] :
% 0.29/0.46 ( ( in @ B @ A )
% 0.29/0.46 & ~ ? [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ B )
% 0.29/0.46 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(wellorderingAx_type,type,
% 0.29/0.46 wellorderingAx: $o ).
% 0.29/0.46
% 0.29/0.46 thf(wellorderingAx,definition,
% 0.29/0.46 ( wellorderingAx
% 0.29/0.46 = ( ! [A: $i] :
% 0.29/0.46 ? [B: $i] :
% 0.29/0.46 ( ! [C: $i] :
% 0.29/0.46 ( ( in @ C @ B )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ C )
% 0.29/0.46 => ( in @ Xx @ A ) ) )
% 0.29/0.46 & ! [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( ( in @ Xx @ A )
% 0.29/0.46 & ( in @ Xy @ A ) )
% 0.29/0.46 => ( ! [C: $i] :
% 0.29/0.46 ( ( in @ C @ B )
% 0.29/0.46 => ( ( in @ Xx @ C )
% 0.29/0.46 <=> ( in @ Xy @ C ) ) )
% 0.29/0.46 => ( Xx = Xy ) ) )
% 0.29/0.46 & ! [C: $i,D: $i] :
% 0.29/0.46 ( ( ( in @ C @ B )
% 0.29/0.46 & ( in @ D @ B ) )
% 0.29/0.46 => ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ C )
% 0.29/0.46 => ( in @ Xx @ D ) )
% 0.29/0.46 | ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ D )
% 0.29/0.46 => ( in @ Xx @ C ) ) ) )
% 0.29/0.46 & ! [C: $i] :
% 0.29/0.46 ( ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ C )
% 0.29/0.46 => ( in @ Xx @ A ) )
% 0.29/0.46 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 0.29/0.46 => ? [D: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ D @ B )
% 0.29/0.46 & ( in @ Xx @ C )
% 0.29/0.46 & ~ ? [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ D )
% 0.29/0.46 & ( in @ Xy @ C ) )
% 0.29/0.46 & ! [E: $i] :
% 0.29/0.46 ( ( in @ E @ B )
% 0.29/0.46 => ( ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ E )
% 0.29/0.46 => ( in @ Xy @ D ) )
% 0.29/0.46 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(descr_type,type,
% 0.29/0.46 descr: ( $i > $o ) > $i ).
% 0.29/0.46
% 0.29/0.46 thf(descrp_type,type,
% 0.29/0.46 descrp: $o ).
% 0.29/0.46
% 0.29/0.46 thf(descrp,definition,
% 0.29/0.46 ( descrp
% 0.29/0.46 = ( ! [Xphi: $i > $o] :
% 0.29/0.46 ( ( exu
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.46 => ( Xphi
% 0.29/0.46 @ ( descr
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(dsetconstr_type,type,
% 0.29/0.46 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.29/0.46
% 0.29/0.46 thf(dsetconstrI_type,type,
% 0.29/0.46 dsetconstrI: $o ).
% 0.29/0.46
% 0.29/0.46 thf(dsetconstrI,definition,
% 0.29/0.46 ( dsetconstrI
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( Xphi @ Xx )
% 0.29/0.46 => ( in @ Xx
% 0.29/0.46 @ ( dsetconstr @ A
% 0.29/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(dsetconstrEL_type,type,
% 0.29/0.46 dsetconstrEL: $o ).
% 0.29/0.46
% 0.29/0.46 thf(dsetconstrEL,definition,
% 0.29/0.46 ( dsetconstrEL
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx
% 0.29/0.46 @ ( dsetconstr @ A
% 0.29/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.29/0.46 => ( in @ Xx @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(dsetconstrER_type,type,
% 0.29/0.46 dsetconstrER: $o ).
% 0.29/0.46
% 0.29/0.46 thf(dsetconstrER,definition,
% 0.29/0.46 ( dsetconstrER
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx
% 0.29/0.46 @ ( dsetconstr @ A
% 0.29/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.29/0.46 => ( Xphi @ Xx ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(exuE1_type,type,
% 0.29/0.46 exuE1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(exuE1,definition,
% 0.29/0.46 ( exuE1
% 0.29/0.46 = ( ! [Xphi: $i > $o] :
% 0.29/0.46 ( ( exu
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.46 => ? [Xx: $i] :
% 0.29/0.46 ( ( Xphi @ Xx )
% 0.29/0.46 & ! [Xy: $i] :
% 0.29/0.46 ( ( Xphi @ Xy )
% 0.29/0.46 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(prop2set_type,type,
% 0.29/0.46 prop2set: $o > $i ).
% 0.29/0.46
% 0.29/0.46 thf(prop2setE_type,type,
% 0.29/0.46 prop2setE: $o ).
% 0.29/0.46
% 0.29/0.46 thf(prop2setE,definition,
% 0.29/0.46 ( prop2setE
% 0.29/0.46 = ( ! [Xphi: $o,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 0.29/0.46 => Xphi ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(emptysetE_type,type,
% 0.29/0.46 emptysetE: $o ).
% 0.29/0.46
% 0.29/0.46 thf(emptysetE,definition,
% 0.29/0.46 ( emptysetE
% 0.29/0.46 = ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ emptyset )
% 0.29/0.46 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(emptysetimpfalse_type,type,
% 0.29/0.46 emptysetimpfalse: $o ).
% 0.29/0.46
% 0.29/0.46 thf(emptysetimpfalse,definition,
% 0.29/0.46 ( emptysetimpfalse
% 0.29/0.46 = ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ emptyset )
% 0.29/0.46 => $false ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(notinemptyset_type,type,
% 0.29/0.46 notinemptyset: $o ).
% 0.29/0.46
% 0.29/0.46 thf(notinemptyset,definition,
% 0.29/0.46 ( notinemptyset
% 0.29/0.46 = ( ! [Xx: $i] :
% 0.29/0.46 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(exuE3e_type,type,
% 0.29/0.46 exuE3e: $o ).
% 0.29/0.46
% 0.29/0.46 thf(exuE3e,definition,
% 0.29/0.46 ( exuE3e
% 0.29/0.46 = ( ! [Xphi: $i > $o] :
% 0.29/0.46 ( ( exu
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.46 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setext_type,type,
% 0.29/0.46 setext: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setext,definition,
% 0.29/0.46 ( setext
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( in @ Xx @ B ) )
% 0.29/0.46 => ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ B )
% 0.29/0.46 => ( in @ Xx @ A ) )
% 0.29/0.46 => ( A = B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(emptyI_type,type,
% 0.29/0.46 emptyI: $o ).
% 0.29/0.46
% 0.29/0.46 thf(emptyI,definition,
% 0.29/0.46 ( emptyI
% 0.29/0.46 = ( ! [A: $i] :
% 0.29/0.46 ( ! [Xx: $i] :
% 0.29/0.46 ~ ( in @ Xx @ A )
% 0.29/0.46 => ( A = emptyset ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(noeltsimpempty_type,type,
% 0.29/0.46 noeltsimpempty: $o ).
% 0.29/0.46
% 0.29/0.46 thf(noeltsimpempty,definition,
% 0.29/0.46 ( noeltsimpempty
% 0.29/0.46 = ( ! [A: $i] :
% 0.29/0.46 ( ! [Xx: $i] :
% 0.29/0.46 ~ ( in @ Xx @ A )
% 0.29/0.46 => ( A = emptyset ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setbeta_type,type,
% 0.29/0.46 setbeta: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setbeta,definition,
% 0.29/0.46 ( setbeta
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( in @ Xx
% 0.29/0.46 @ ( dsetconstr @ A
% 0.29/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.29/0.46 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(nonempty_type,type,
% 0.29/0.46 nonempty: $i > $o ).
% 0.29/0.46
% 0.29/0.46 thf(nonempty,definition,
% 0.29/0.46 ( nonempty
% 0.29/0.46 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(nonemptyE1_type,type,
% 0.29/0.46 nonemptyE1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(nonemptyE1,definition,
% 0.29/0.46 ( nonemptyE1
% 0.29/0.46 = ( ! [A: $i] :
% 0.29/0.46 ( ( nonempty @ A )
% 0.29/0.46 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(nonemptyI_type,type,
% 0.29/0.46 nonemptyI: $o ).
% 0.29/0.46
% 0.29/0.46 thf(nonemptyI,definition,
% 0.29/0.46 ( nonemptyI
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( Xphi @ Xx )
% 0.29/0.46 => ( nonempty
% 0.29/0.46 @ ( dsetconstr @ A
% 0.29/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(nonemptyI1_type,type,
% 0.29/0.46 nonemptyI1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(nonemptyI1,definition,
% 0.29/0.46 ( nonemptyI1
% 0.29/0.46 = ( ! [A: $i] :
% 0.29/0.46 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.29/0.46 => ( nonempty @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoinIL_type,type,
% 0.29/0.46 setadjoinIL: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoinIL,definition,
% 0.29/0.46 ( setadjoinIL
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(emptyinunitempty_type,type,
% 0.29/0.46 emptyinunitempty: $o ).
% 0.29/0.46
% 0.29/0.46 thf(emptyinunitempty,definition,
% 0.29/0.46 ( emptyinunitempty
% 0.29/0.46 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoinIR_type,type,
% 0.29/0.46 setadjoinIR: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoinIR,definition,
% 0.29/0.46 ( setadjoinIR
% 0.29/0.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ A )
% 0.29/0.46 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoinE_type,type,
% 0.29/0.46 setadjoinE: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoinE,definition,
% 0.29/0.46 ( setadjoinE
% 0.29/0.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.29/0.46 => ! [Xphi: $o] :
% 0.29/0.46 ( ( ( Xy = Xx )
% 0.29/0.46 => Xphi )
% 0.29/0.46 => ( ( ( in @ Xy @ A )
% 0.29/0.46 => Xphi )
% 0.29/0.46 => Xphi ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoinOr_type,type,
% 0.29/0.46 setadjoinOr: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoinOr,definition,
% 0.29/0.46 ( setadjoinOr
% 0.29/0.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.29/0.46 => ( ( Xy = Xx )
% 0.29/0.46 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setoftrueEq_type,type,
% 0.29/0.46 setoftrueEq: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setoftrueEq,definition,
% 0.29/0.46 ( setoftrueEq
% 0.29/0.46 = ( ! [A: $i] :
% 0.29/0.46 ( ( dsetconstr @ A
% 0.29/0.46 @ ^ [Xx: $i] : $true )
% 0.29/0.46 = A ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(powersetI_type,type,
% 0.29/0.46 powersetI: $o ).
% 0.29/0.46
% 0.29/0.46 thf(powersetI,definition,
% 0.29/0.46 ( powersetI
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ B )
% 0.29/0.46 => ( in @ Xx @ A ) )
% 0.29/0.46 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(emptyinPowerset_type,type,
% 0.29/0.46 emptyinPowerset: $o ).
% 0.29/0.46
% 0.29/0.46 thf(emptyinPowerset,definition,
% 0.29/0.46 ( emptyinPowerset
% 0.29/0.46 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(emptyInPowerset_type,type,
% 0.29/0.46 emptyInPowerset: $o ).
% 0.29/0.46
% 0.29/0.46 thf(emptyInPowerset,definition,
% 0.29/0.46 ( emptyInPowerset
% 0.29/0.46 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(powersetE_type,type,
% 0.29/0.46 powersetE: $o ).
% 0.29/0.46
% 0.29/0.46 thf(powersetE,definition,
% 0.29/0.46 ( powersetE
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ B @ ( powerset @ A ) )
% 0.29/0.46 => ( ( in @ Xx @ B )
% 0.29/0.46 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setunionI_type,type,
% 0.29/0.46 setunionI: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setunionI,definition,
% 0.29/0.46 ( setunionI
% 0.29/0.46 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.29/0.46 ( ( in @ Xx @ B )
% 0.29/0.46 => ( ( in @ B @ A )
% 0.29/0.46 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setunionE_type,type,
% 0.29/0.46 setunionE: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setunionE,definition,
% 0.29/0.46 ( setunionE
% 0.29/0.46 = ( ! [A: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ ( setunion @ A ) )
% 0.29/0.46 => ! [Xphi: $o] :
% 0.29/0.46 ( ! [B: $i] :
% 0.29/0.46 ( ( in @ Xx @ B )
% 0.29/0.46 => ( ( in @ B @ A )
% 0.29/0.46 => Xphi ) )
% 0.29/0.46 => Xphi ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(subPowSU_type,type,
% 0.29/0.46 subPowSU: $o ).
% 0.29/0.46
% 0.29/0.46 thf(subPowSU,definition,
% 0.29/0.46 ( subPowSU
% 0.29/0.46 = ( ! [A: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(exuE2_type,type,
% 0.29/0.46 exuE2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(exuE2,definition,
% 0.29/0.46 ( exuE2
% 0.29/0.46 = ( ! [Xphi: $i > $o] :
% 0.29/0.46 ( ( exu
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.46 => ? [Xx: $i] :
% 0.29/0.46 ! [Xy: $i] :
% 0.29/0.46 ( ( Xphi @ Xy )
% 0.29/0.46 <=> ( Xy = Xx ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(nonemptyImpWitness_type,type,
% 0.29/0.46 nonemptyImpWitness: $o ).
% 0.29/0.46
% 0.29/0.46 thf(nonemptyImpWitness,definition,
% 0.29/0.46 ( nonemptyImpWitness
% 0.29/0.46 = ( ! [A: $i] :
% 0.29/0.46 ( ( nonempty @ A )
% 0.29/0.46 => ? [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 & $true ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(uniqinunit_type,type,
% 0.29/0.46 uniqinunit: $o ).
% 0.29/0.46
% 0.29/0.46 thf(uniqinunit,definition,
% 0.29/0.46 ( uniqinunit
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.29/0.46 => ( Xx = Xy ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(notinsingleton_type,type,
% 0.29/0.46 notinsingleton: $o ).
% 0.29/0.46
% 0.29/0.46 thf(notinsingleton,definition,
% 0.29/0.46 ( notinsingleton
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( Xx != Xy )
% 0.29/0.46 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(eqinunit_type,type,
% 0.29/0.46 eqinunit: $o ).
% 0.29/0.46
% 0.29/0.46 thf(eqinunit,definition,
% 0.29/0.46 ( eqinunit
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( Xx = Xy )
% 0.29/0.46 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(singletonsswitch_type,type,
% 0.29/0.46 singletonsswitch: $o ).
% 0.29/0.46
% 0.29/0.46 thf(singletonsswitch,definition,
% 0.29/0.46 ( singletonsswitch
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.29/0.46 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(upairsetE_type,type,
% 0.29/0.46 upairsetE: $o ).
% 0.29/0.46
% 0.29/0.46 thf(upairsetE,definition,
% 0.29/0.46 ( upairsetE
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.29/0.46 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.29/0.46 => ( ( Xz = Xx )
% 0.29/0.46 | ( Xz = Xy ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(upairsetIL_type,type,
% 0.29/0.46 upairsetIL: $o ).
% 0.29/0.46
% 0.29/0.46 thf(upairsetIL,definition,
% 0.29/0.46 ( upairsetIL
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(upairsetIR_type,type,
% 0.29/0.46 upairsetIR: $o ).
% 0.29/0.46
% 0.29/0.46 thf(upairsetIR,definition,
% 0.29/0.46 ( upairsetIR
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(emptyE1_type,type,
% 0.29/0.46 emptyE1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(emptyE1,definition,
% 0.29/0.46 ( emptyE1
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.46 ( ? [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 & ( Xphi @ Xx ) )
% 0.29/0.46 => ( ( ( dsetconstr @ A
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.46 = emptyset )
% 0.29/0.46 => $false ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(vacuousDall_type,type,
% 0.29/0.46 vacuousDall: $o ).
% 0.29/0.46
% 0.29/0.46 thf(vacuousDall,definition,
% 0.29/0.46 ( vacuousDall
% 0.29/0.46 = ( ! [Xphi: $i > $o,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ emptyset )
% 0.29/0.46 => ( Xphi @ Xx ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(quantDeMorgan1_type,type,
% 0.29/0.46 quantDeMorgan1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(quantDeMorgan1,definition,
% 0.29/0.46 ( quantDeMorgan1
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.46 ( ~ ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( Xphi @ Xx ) )
% 0.29/0.46 => ? [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(quantDeMorgan2_type,type,
% 0.29/0.46 quantDeMorgan2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(quantDeMorgan2,definition,
% 0.29/0.46 ( quantDeMorgan2
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.46 ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ~ ( Xphi @ Xx ) )
% 0.29/0.46 => ~ ? [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(quantDeMorgan3_type,type,
% 0.29/0.46 quantDeMorgan3: $o ).
% 0.29/0.46
% 0.29/0.46 thf(quantDeMorgan3,definition,
% 0.29/0.46 ( quantDeMorgan3
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.46 ( ~ ? [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 & ( Xphi @ Xx ) )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(quantDeMorgan4_type,type,
% 0.29/0.46 quantDeMorgan4: $o ).
% 0.29/0.46
% 0.29/0.46 thf(quantDeMorgan4,definition,
% 0.29/0.46 ( quantDeMorgan4
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.46 ( ? [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 & ~ ( Xphi @ Xx ) )
% 0.29/0.46 => ~ ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(prop2setI_type,type,
% 0.29/0.46 prop2setI: $o ).
% 0.29/0.46
% 0.29/0.46 thf(prop2setI,definition,
% 0.29/0.46 ( prop2setI
% 0.29/0.46 = ( ! [Xphi: $o] :
% 0.29/0.46 ( Xphi
% 0.29/0.46 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(set2prop_type,type,
% 0.29/0.46 set2prop: $i > $o ).
% 0.29/0.46
% 0.29/0.46 thf(prop2set2propI_type,type,
% 0.29/0.46 prop2set2propI: $o ).
% 0.29/0.46
% 0.29/0.46 thf(prop2set2propI,definition,
% 0.29/0.46 ( prop2set2propI
% 0.29/0.46 = ( ! [Xphi: $o] :
% 0.29/0.46 ( Xphi
% 0.29/0.46 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(notdexE_type,type,
% 0.29/0.46 notdexE: $o ).
% 0.29/0.46
% 0.29/0.46 thf(notdexE,definition,
% 0.29/0.46 ( notdexE
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.46 ( ~ ? [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 & ( Xphi @ Xx ) )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(notdallE_type,type,
% 0.29/0.46 notdallE: $o ).
% 0.29/0.46
% 0.29/0.46 thf(notdallE,definition,
% 0.29/0.46 ( notdallE
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.46 ( ~ ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( Xphi @ Xx ) )
% 0.29/0.46 => ? [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(exuI1_type,type,
% 0.29/0.46 exuI1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(exuI1,definition,
% 0.29/0.46 ( exuI1
% 0.29/0.46 = ( ! [Xphi: $i > $o] :
% 0.29/0.46 ( ? [Xx: $i] :
% 0.29/0.46 ( ( Xphi @ Xx )
% 0.29/0.46 & ! [Xy: $i] :
% 0.29/0.46 ( ( Xphi @ Xy )
% 0.29/0.46 => ( Xx = Xy ) ) )
% 0.29/0.46 => ( exu
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(exuI3_type,type,
% 0.29/0.46 exuI3: $o ).
% 0.29/0.46
% 0.29/0.46 thf(exuI3,definition,
% 0.29/0.46 ( exuI3
% 0.29/0.46 = ( ! [Xphi: $i > $o] :
% 0.29/0.46 ( ? [Xx: $i] : ( Xphi @ Xx )
% 0.29/0.46 => ( ! [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( Xphi @ Xx )
% 0.29/0.46 => ( ( Xphi @ Xy )
% 0.29/0.46 => ( Xx = Xy ) ) )
% 0.29/0.46 => ( exu
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(exuI2_type,type,
% 0.29/0.46 exuI2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(exuI2,definition,
% 0.29/0.46 ( exuI2
% 0.29/0.46 = ( ! [Xphi: $i > $o] :
% 0.29/0.46 ( ? [Xx: $i] :
% 0.29/0.46 ! [Xy: $i] :
% 0.29/0.46 ( ( Xphi @ Xy )
% 0.29/0.46 <=> ( Xy = Xx ) )
% 0.29/0.46 => ( exu
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(inCongP_type,type,
% 0.29/0.46 inCongP: $o ).
% 0.29/0.46
% 0.29/0.46 thf(inCongP,definition,
% 0.29/0.46 ( inCongP
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( A = B )
% 0.29/0.46 => ! [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( Xx = Xy )
% 0.29/0.46 => ( ( in @ Xx @ A )
% 0.29/0.46 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(in__Cong_type,type,
% 0.29/0.46 in__Cong: $o ).
% 0.29/0.46
% 0.29/0.46 thf(in__Cong,definition,
% 0.29/0.46 ( in__Cong
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( A = B )
% 0.29/0.46 => ! [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( Xx = Xy )
% 0.29/0.46 => ( ( in @ Xx @ A )
% 0.29/0.46 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(exuE3u_type,type,
% 0.29/0.46 exuE3u: $o ).
% 0.29/0.46
% 0.29/0.46 thf(exuE3u,definition,
% 0.29/0.46 ( exuE3u
% 0.29/0.46 = ( ! [Xphi: $i > $o] :
% 0.29/0.46 ( ( exu
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.46 => ! [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( Xphi @ Xx )
% 0.29/0.46 => ( ( Xphi @ Xy )
% 0.29/0.46 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(exu__Cong_type,type,
% 0.29/0.46 exu__Cong: $o ).
% 0.29/0.46
% 0.29/0.46 thf(exu__Cong,definition,
% 0.29/0.46 ( exu__Cong
% 0.29/0.46 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.29/0.46 ( ! [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( Xx = Xy )
% 0.29/0.46 => ( ( Xphi @ Xx )
% 0.29/0.46 <=> ( Xpsi @ Xy ) ) )
% 0.29/0.46 => ( ( exu
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.46 <=> ( exu
% 0.29/0.46 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(emptyset__Cong_type,type,
% 0.29/0.46 emptyset__Cong: $o ).
% 0.29/0.46
% 0.29/0.46 thf(emptyset__Cong,definition,
% 0.29/0.46 ( emptyset__Cong
% 0.29/0.46 = ( emptyset = emptyset ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoin__Cong_type,type,
% 0.29/0.46 setadjoin__Cong: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoin__Cong,definition,
% 0.29/0.46 ( setadjoin__Cong
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( Xx = Xy )
% 0.29/0.46 => ! [Xz: $i,Xu: $i] :
% 0.29/0.46 ( ( Xz = Xu )
% 0.29/0.46 => ( ( setadjoin @ Xx @ Xz )
% 0.29/0.46 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(powerset__Cong_type,type,
% 0.29/0.46 powerset__Cong: $o ).
% 0.29/0.46
% 0.29/0.46 thf(powerset__Cong,definition,
% 0.29/0.46 ( powerset__Cong
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( A = B )
% 0.29/0.46 => ( ( powerset @ A )
% 0.29/0.46 = ( powerset @ B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setunion__Cong_type,type,
% 0.29/0.46 setunion__Cong: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setunion__Cong,definition,
% 0.29/0.46 ( setunion__Cong
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( A = B )
% 0.29/0.46 => ( ( setunion @ A )
% 0.29/0.46 = ( setunion @ B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(omega__Cong_type,type,
% 0.29/0.46 omega__Cong: $o ).
% 0.29/0.46
% 0.29/0.46 thf(omega__Cong,definition,
% 0.29/0.46 ( omega__Cong
% 0.29/0.46 = ( omega = omega ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(exuEu_type,type,
% 0.29/0.46 exuEu: $o ).
% 0.29/0.46
% 0.29/0.46 thf(exuEu,definition,
% 0.29/0.46 ( exuEu
% 0.29/0.46 = ( ! [Xphi: $i > $o] :
% 0.29/0.46 ( ( exu
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.46 => ! [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( Xphi @ Xx )
% 0.29/0.46 => ( ( Xphi @ Xy )
% 0.29/0.46 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(descr__Cong_type,type,
% 0.29/0.46 descr__Cong: $o ).
% 0.29/0.46
% 0.29/0.46 thf(descr__Cong,definition,
% 0.29/0.46 ( descr__Cong
% 0.29/0.46 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.29/0.46 ( ! [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( Xx = Xy )
% 0.29/0.46 => ( ( Xphi @ Xx )
% 0.29/0.46 <=> ( Xpsi @ Xy ) ) )
% 0.29/0.46 => ( ( exu
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.46 => ( ( exu
% 0.29/0.46 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 0.29/0.46 => ( ( descr
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.46 = ( descr
% 0.29/0.46 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(dsetconstr__Cong_type,type,
% 0.29/0.46 dsetconstr__Cong: $o ).
% 0.29/0.46
% 0.29/0.46 thf(dsetconstr__Cong,definition,
% 0.29/0.46 ( dsetconstr__Cong
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( A = B )
% 0.29/0.46 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.29/0.46 ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ B )
% 0.29/0.46 => ( ( Xx = Xy )
% 0.29/0.46 => ( ( Xphi @ Xx )
% 0.29/0.46 <=> ( Xpsi @ Xy ) ) ) ) )
% 0.29/0.46 => ( ( dsetconstr @ A
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.46 = ( dsetconstr @ B
% 0.29/0.46 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(subset_type,type,
% 0.29/0.46 subset: $i > $i > $o ).
% 0.29/0.46
% 0.29/0.46 thf(disjoint_type,type,
% 0.29/0.46 disjoint: $i > $i > $o ).
% 0.29/0.46
% 0.29/0.46 thf(setsmeet_type,type,
% 0.29/0.46 setsmeet: $i > $i > $o ).
% 0.29/0.46
% 0.29/0.46 thf(subsetI1_type,type,
% 0.29/0.46 subsetI1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(subsetI1,definition,
% 0.29/0.46 ( subsetI1
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( in @ Xx @ B ) )
% 0.29/0.46 => ( subset @ A @ B ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(eqimpsubset2_type,type,
% 0.29/0.46 eqimpsubset2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(eqimpsubset2,definition,
% 0.29/0.46 ( eqimpsubset2
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( A = B )
% 0.29/0.46 => ( subset @ B @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(eqimpsubset1_type,type,
% 0.29/0.46 eqimpsubset1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(eqimpsubset1,definition,
% 0.29/0.46 ( eqimpsubset1
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( A = B )
% 0.29/0.46 => ( subset @ A @ B ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(subsetI2_type,type,
% 0.29/0.46 subsetI2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(subsetI2,definition,
% 0.29/0.46 ( subsetI2
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( in @ Xx @ B ) )
% 0.29/0.46 => ( subset @ A @ B ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(emptysetsubset_type,type,
% 0.29/0.46 emptysetsubset: $o ).
% 0.29/0.46
% 0.29/0.46 thf(emptysetsubset,definition,
% 0.29/0.46 ( emptysetsubset
% 0.29/0.46 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(subsetE_type,type,
% 0.29/0.46 subsetE: $o ).
% 0.29/0.46
% 0.29/0.46 thf(subsetE,definition,
% 0.29/0.46 ( subsetE
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( subset @ A @ B )
% 0.29/0.46 => ( ( in @ Xx @ A )
% 0.29/0.46 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(subsetE2_type,type,
% 0.29/0.46 subsetE2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(subsetE2,definition,
% 0.29/0.46 ( subsetE2
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( subset @ A @ B )
% 0.29/0.46 => ( ~ ( in @ Xx @ B )
% 0.29/0.46 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(notsubsetI_type,type,
% 0.29/0.46 notsubsetI: $o ).
% 0.29/0.46
% 0.29/0.46 thf(notsubsetI,definition,
% 0.29/0.46 ( notsubsetI
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ~ ( in @ Xx @ B )
% 0.29/0.46 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(notequalI1_type,type,
% 0.29/0.46 notequalI1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(notequalI1,definition,
% 0.29/0.46 ( notequalI1
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ~ ( subset @ A @ B )
% 0.29/0.46 => ( A != B ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(notequalI2_type,type,
% 0.29/0.46 notequalI2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(notequalI2,definition,
% 0.29/0.46 ( notequalI2
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ~ ( in @ Xx @ B )
% 0.29/0.46 => ( A != B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(subsetRefl_type,type,
% 0.29/0.46 subsetRefl: $o ).
% 0.29/0.46
% 0.29/0.46 thf(subsetRefl,definition,
% 0.29/0.46 ( subsetRefl
% 0.29/0.46 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(subsetTrans_type,type,
% 0.29/0.46 subsetTrans: $o ).
% 0.29/0.46
% 0.29/0.46 thf(subsetTrans,definition,
% 0.29/0.46 ( subsetTrans
% 0.29/0.46 = ( ! [A: $i,B: $i,C: $i] :
% 0.29/0.46 ( ( subset @ A @ B )
% 0.29/0.46 => ( ( subset @ B @ C )
% 0.29/0.46 => ( subset @ A @ C ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoinSub_type,type,
% 0.29/0.46 setadjoinSub: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoinSub,definition,
% 0.29/0.46 ( setadjoinSub
% 0.29/0.46 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoinSub2_type,type,
% 0.29/0.46 setadjoinSub2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoinSub2,definition,
% 0.29/0.46 ( setadjoinSub2
% 0.29/0.46 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.29/0.46 ( ( subset @ A @ B )
% 0.29/0.46 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(subset2powerset_type,type,
% 0.29/0.46 subset2powerset: $o ).
% 0.29/0.46
% 0.29/0.46 thf(subset2powerset,definition,
% 0.29/0.46 ( subset2powerset
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( subset @ A @ B )
% 0.29/0.46 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setextsub_type,type,
% 0.29/0.46 setextsub: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setextsub,definition,
% 0.29/0.46 ( setextsub
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( subset @ A @ B )
% 0.29/0.46 => ( ( subset @ B @ A )
% 0.29/0.46 => ( A = B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(subsetemptysetimpeq_type,type,
% 0.29/0.46 subsetemptysetimpeq: $o ).
% 0.29/0.46
% 0.29/0.46 thf(subsetemptysetimpeq,definition,
% 0.29/0.46 ( subsetemptysetimpeq
% 0.29/0.46 = ( ! [A: $i] :
% 0.29/0.46 ( ( subset @ A @ emptyset )
% 0.29/0.46 => ( A = emptyset ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(powersetI1_type,type,
% 0.29/0.46 powersetI1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(powersetI1,definition,
% 0.29/0.46 ( powersetI1
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( subset @ B @ A )
% 0.29/0.46 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(powersetE1_type,type,
% 0.29/0.46 powersetE1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(powersetE1,definition,
% 0.29/0.46 ( powersetE1
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( in @ B @ ( powerset @ A ) )
% 0.29/0.46 => ( subset @ B @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(inPowerset_type,type,
% 0.29/0.46 inPowerset: $o ).
% 0.29/0.46
% 0.29/0.46 thf(inPowerset,definition,
% 0.29/0.46 ( inPowerset
% 0.29/0.46 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(powersetsubset_type,type,
% 0.29/0.46 powersetsubset: $o ).
% 0.29/0.46
% 0.29/0.46 thf(powersetsubset,definition,
% 0.29/0.46 ( powersetsubset
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( subset @ A @ B )
% 0.29/0.46 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(sepInPowerset_type,type,
% 0.29/0.46 sepInPowerset: $o ).
% 0.29/0.46
% 0.29/0.46 thf(sepInPowerset,definition,
% 0.29/0.46 ( sepInPowerset
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.46 ( in
% 0.29/0.46 @ ( dsetconstr @ A
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.46 @ ( powerset @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(sepSubset_type,type,
% 0.29/0.46 sepSubset: $o ).
% 0.29/0.46
% 0.29/0.46 thf(sepSubset,definition,
% 0.29/0.46 ( sepSubset
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.46 ( subset
% 0.29/0.46 @ ( dsetconstr @ A
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.46 @ A ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binunion_type,type,
% 0.29/0.46 binunion: $i > $i > $i ).
% 0.29/0.46
% 0.29/0.46 thf(binunionIL_type,type,
% 0.29/0.46 binunionIL: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binunionIL,definition,
% 0.29/0.46 ( binunionIL
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(upairset2IR_type,type,
% 0.29/0.46 upairset2IR: $o ).
% 0.29/0.46
% 0.29/0.46 thf(upairset2IR,definition,
% 0.29/0.46 ( upairset2IR
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binunionIR_type,type,
% 0.29/0.46 binunionIR: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binunionIR,definition,
% 0.29/0.46 ( binunionIR
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ B )
% 0.29/0.46 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binunionEcases_type,type,
% 0.29/0.46 binunionEcases: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binunionEcases,definition,
% 0.29/0.46 ( binunionEcases
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 0.29/0.46 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.29/0.46 => ( ( ( in @ Xx @ A )
% 0.29/0.46 => Xphi )
% 0.29/0.46 => ( ( ( in @ Xx @ B )
% 0.29/0.46 => Xphi )
% 0.29/0.46 => Xphi ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binunionE_type,type,
% 0.29/0.46 binunionE: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binunionE,definition,
% 0.29/0.46 ( binunionE
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.29/0.46 => ( ( in @ Xx @ A )
% 0.29/0.46 | ( in @ Xx @ B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binunionLsub_type,type,
% 0.29/0.46 binunionLsub: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binunionLsub,definition,
% 0.29/0.46 ( binunionLsub
% 0.29/0.46 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binunionRsub_type,type,
% 0.29/0.46 binunionRsub: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binunionRsub,definition,
% 0.29/0.46 ( binunionRsub
% 0.29/0.46 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binintersect_type,type,
% 0.29/0.46 binintersect: $i > $i > $i ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectI_type,type,
% 0.29/0.46 binintersectI: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectI,definition,
% 0.29/0.46 ( binintersectI
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( in @ Xx @ B )
% 0.29/0.46 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectSubset5_type,type,
% 0.29/0.46 binintersectSubset5: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectSubset5,definition,
% 0.29/0.46 ( binintersectSubset5
% 0.29/0.46 = ( ! [A: $i,B: $i,C: $i] :
% 0.29/0.46 ( ( subset @ C @ A )
% 0.29/0.46 => ( ( subset @ C @ B )
% 0.29/0.46 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectEL_type,type,
% 0.29/0.46 binintersectEL: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectEL,definition,
% 0.29/0.46 ( binintersectEL
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.29/0.46 => ( in @ Xx @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectLsub_type,type,
% 0.29/0.46 binintersectLsub: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectLsub,definition,
% 0.29/0.46 ( binintersectLsub
% 0.29/0.46 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectSubset2_type,type,
% 0.29/0.46 binintersectSubset2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectSubset2,definition,
% 0.29/0.46 ( binintersectSubset2
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( subset @ A @ B )
% 0.29/0.46 => ( ( binintersect @ A @ B )
% 0.29/0.46 = A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectSubset3_type,type,
% 0.29/0.46 binintersectSubset3: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectSubset3,definition,
% 0.29/0.46 ( binintersectSubset3
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( ( binintersect @ A @ B )
% 0.29/0.46 = B )
% 0.29/0.46 => ( subset @ B @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectER_type,type,
% 0.29/0.46 binintersectER: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectER,definition,
% 0.29/0.46 ( binintersectER
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.29/0.46 => ( in @ Xx @ B ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(disjointsetsI1_type,type,
% 0.29/0.46 disjointsetsI1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(disjointsetsI1,definition,
% 0.29/0.46 ( disjointsetsI1
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ~ ? [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 & ( in @ Xx @ B ) )
% 0.29/0.46 => ( ( binintersect @ A @ B )
% 0.29/0.46 = emptyset ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectRsub_type,type,
% 0.29/0.46 binintersectRsub: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectRsub,definition,
% 0.29/0.46 ( binintersectRsub
% 0.29/0.46 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectSubset4_type,type,
% 0.29/0.46 binintersectSubset4: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectSubset4,definition,
% 0.29/0.46 ( binintersectSubset4
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( subset @ B @ A )
% 0.29/0.46 => ( ( binintersect @ A @ B )
% 0.29/0.46 = B ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectSubset1_type,type,
% 0.29/0.46 binintersectSubset1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectSubset1,definition,
% 0.29/0.46 ( binintersectSubset1
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( ( binintersect @ A @ B )
% 0.29/0.46 = A )
% 0.29/0.46 => ( subset @ A @ B ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(bs114d_type,type,
% 0.29/0.46 bs114d: $o ).
% 0.29/0.46
% 0.29/0.46 thf(bs114d,definition,
% 0.29/0.46 ( bs114d
% 0.29/0.46 = ( ! [A: $i,B: $i,C: $i] :
% 0.29/0.46 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 0.29/0.46 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(regular_type,type,
% 0.29/0.46 regular: $i > $o ).
% 0.29/0.46
% 0.29/0.46 thf(setminus_type,type,
% 0.29/0.46 setminus: $i > $i > $i ).
% 0.29/0.46
% 0.29/0.46 thf(setminusI_type,type,
% 0.29/0.46 setminusI: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setminusI,definition,
% 0.29/0.46 ( setminusI
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ~ ( in @ Xx @ B )
% 0.29/0.46 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setminusEL_type,type,
% 0.29/0.46 setminusEL: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setminusEL,definition,
% 0.29/0.46 ( setminusEL
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.29/0.46 => ( in @ Xx @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setminusER_type,type,
% 0.29/0.46 setminusER: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setminusER,definition,
% 0.29/0.46 ( setminusER
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.29/0.46 => ~ ( in @ Xx @ B ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setminusSubset2_type,type,
% 0.29/0.46 setminusSubset2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setminusSubset2,definition,
% 0.29/0.46 ( setminusSubset2
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( subset @ A @ B )
% 0.29/0.46 => ( ( setminus @ A @ B )
% 0.29/0.46 = emptyset ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setminusERneg_type,type,
% 0.29/0.46 setminusERneg: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setminusERneg,definition,
% 0.29/0.46 ( setminusERneg
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.29/0.46 => ( ( in @ Xx @ A )
% 0.29/0.46 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setminusELneg_type,type,
% 0.29/0.46 setminusELneg: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setminusELneg,definition,
% 0.29/0.46 ( setminusELneg
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.29/0.46 => ( ~ ( in @ Xx @ B )
% 0.29/0.46 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setminusILneg_type,type,
% 0.29/0.46 setminusILneg: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setminusILneg,definition,
% 0.29/0.46 ( setminusILneg
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ~ ( in @ Xx @ A )
% 0.29/0.46 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setminusIRneg_type,type,
% 0.29/0.46 setminusIRneg: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setminusIRneg,definition,
% 0.29/0.46 ( setminusIRneg
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ B )
% 0.29/0.46 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setminusLsub_type,type,
% 0.29/0.46 setminusLsub: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setminusLsub,definition,
% 0.29/0.46 ( setminusLsub
% 0.29/0.46 = ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setminusSubset1_type,type,
% 0.29/0.46 setminusSubset1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setminusSubset1,definition,
% 0.29/0.46 ( setminusSubset1
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( ( setminus @ A @ B )
% 0.29/0.46 = emptyset )
% 0.29/0.46 => ( subset @ A @ B ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(symdiff_type,type,
% 0.29/0.46 symdiff: $i > $i > $i ).
% 0.29/0.46
% 0.29/0.46 thf(symdiffE_type,type,
% 0.29/0.46 symdiffE: $o ).
% 0.29/0.46
% 0.29/0.46 thf(symdiffE,definition,
% 0.29/0.46 ( symdiffE
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ ( symdiff @ A @ B ) )
% 0.29/0.46 => ! [Xphi: $o] :
% 0.29/0.46 ( ( ( in @ Xx @ A )
% 0.29/0.46 => ( ~ ( in @ Xx @ B )
% 0.29/0.46 => Xphi ) )
% 0.29/0.46 => ( ( ~ ( in @ Xx @ A )
% 0.29/0.46 => ( ( in @ Xx @ B )
% 0.29/0.46 => Xphi ) )
% 0.29/0.46 => Xphi ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(symdiffI1_type,type,
% 0.29/0.46 symdiffI1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(symdiffI1,definition,
% 0.29/0.46 ( symdiffI1
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ~ ( in @ Xx @ B )
% 0.29/0.46 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(symdiffI2_type,type,
% 0.29/0.46 symdiffI2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(symdiffI2,definition,
% 0.29/0.46 ( symdiffI2
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ~ ( in @ Xx @ A )
% 0.29/0.46 => ( ( in @ Xx @ B )
% 0.29/0.46 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(symdiffIneg1_type,type,
% 0.29/0.46 symdiffIneg1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(symdiffIneg1,definition,
% 0.29/0.46 ( symdiffIneg1
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( in @ Xx @ B )
% 0.29/0.46 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(symdiffIneg2_type,type,
% 0.29/0.46 symdiffIneg2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(symdiffIneg2,definition,
% 0.29/0.46 ( symdiffIneg2
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ~ ( in @ Xx @ A )
% 0.29/0.46 => ( ~ ( in @ Xx @ B )
% 0.29/0.46 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(iskpair_type,type,
% 0.29/0.46 iskpair: $i > $o ).
% 0.29/0.46
% 0.29/0.46 thf(iskpair,definition,
% 0.29/0.46 ( iskpair
% 0.29/0.46 = ( ^ [A: $i] :
% 0.29/0.46 ? [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ ( setunion @ A ) )
% 0.29/0.46 & ? [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ ( setunion @ A ) )
% 0.29/0.46 & ( A
% 0.29/0.46 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(secondinupair_type,type,
% 0.29/0.46 secondinupair: $o ).
% 0.29/0.46
% 0.29/0.46 thf(secondinupair,definition,
% 0.29/0.46 ( secondinupair
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setukpairIL_type,type,
% 0.29/0.46 setukpairIL: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setukpairIL,definition,
% 0.29/0.46 ( setukpairIL
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setukpairIR_type,type,
% 0.29/0.46 setukpairIR: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setukpairIR,definition,
% 0.29/0.46 ( setukpairIR
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(kpairiskpair_type,type,
% 0.29/0.46 kpairiskpair: $o ).
% 0.29/0.46
% 0.29/0.46 thf(kpairiskpair,definition,
% 0.29/0.46 ( kpairiskpair
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(kpair_type,type,
% 0.29/0.46 kpair: $i > $i > $i ).
% 0.29/0.46
% 0.29/0.46 thf(kpair,definition,
% 0.29/0.46 ( kpair
% 0.29/0.46 = ( ^ [Xx: $i,Xy: $i] : ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(kpairp_type,type,
% 0.29/0.46 kpairp: $o ).
% 0.29/0.46
% 0.29/0.46 thf(kpairp,definition,
% 0.29/0.46 ( kpairp
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(cartprod_type,type,
% 0.29/0.46 cartprod: $i > $i > $i ).
% 0.29/0.46
% 0.29/0.46 thf(cartprod,definition,
% 0.29/0.46 ( cartprod
% 0.29/0.46 = ( ^ [A: $i,B: $i] :
% 0.29/0.46 ( dsetconstr @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) )
% 0.29/0.46 @ ^ [Xx: $i] :
% 0.29/0.46 ? [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ A )
% 0.29/0.46 & ? [Xz: $i] :
% 0.29/0.46 ( ( in @ Xz @ B )
% 0.29/0.46 & ( Xx
% 0.29/0.46 = ( kpair @ Xy @ Xz ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(singletonsubset_type,type,
% 0.29/0.46 singletonsubset: $o ).
% 0.29/0.46
% 0.29/0.46 thf(singletonsubset,definition,
% 0.29/0.46 ( singletonsubset
% 0.29/0.46 = ( ! [A: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(singletoninpowerset_type,type,
% 0.29/0.46 singletoninpowerset: $o ).
% 0.29/0.46
% 0.29/0.46 thf(singletoninpowerset,definition,
% 0.29/0.46 ( singletoninpowerset
% 0.29/0.46 = ( ! [A: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(singletoninpowunion_type,type,
% 0.29/0.46 singletoninpowunion: $o ).
% 0.29/0.46
% 0.29/0.46 thf(singletoninpowunion,definition,
% 0.29/0.46 ( singletoninpowunion
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(upairset2E_type,type,
% 0.29/0.46 upairset2E: $o ).
% 0.29/0.46
% 0.29/0.46 thf(upairset2E,definition,
% 0.29/0.46 ( upairset2E
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.29/0.46 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.29/0.46 => ( ( Xz = Xx )
% 0.29/0.46 | ( Xz = Xy ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(upairsubunion_type,type,
% 0.29/0.46 upairsubunion: $o ).
% 0.29/0.46
% 0.29/0.46 thf(upairsubunion,definition,
% 0.29/0.46 ( upairsubunion
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ B )
% 0.29/0.46 => ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(upairinpowunion_type,type,
% 0.29/0.46 upairinpowunion: $o ).
% 0.29/0.46
% 0.29/0.46 thf(upairinpowunion,definition,
% 0.29/0.46 ( upairinpowunion
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ B )
% 0.29/0.46 => ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(ubforcartprodlem1,conjecture,
% 0.29/0.46 ( setextAx
% 0.29/0.46 => ( emptysetAx
% 0.29/0.46 => ( setadjoinAx
% 0.29/0.46 => ( powersetAx
% 0.29/0.46 => ( setunionAx
% 0.29/0.46 => ( omega0Ax
% 0.29/0.46 => ( omegaSAx
% 0.29/0.46 => ( omegaIndAx
% 0.29/0.46 => ( replAx
% 0.29/0.46 => ( foundationAx
% 0.29/0.46 => ( wellorderingAx
% 0.29/0.46 => ( descrp
% 0.29/0.46 => ( dsetconstrI
% 0.29/0.46 => ( dsetconstrEL
% 0.29/0.46 => ( dsetconstrER
% 0.29/0.46 => ( exuE1
% 0.29/0.46 => ( prop2setE
% 0.29/0.46 => ( emptysetE
% 0.29/0.46 => ( emptysetimpfalse
% 0.29/0.46 => ( notinemptyset
% 0.29/0.46 => ( exuE3e
% 0.29/0.46 => ( setext
% 0.29/0.46 => ( emptyI
% 0.29/0.46 => ( noeltsimpempty
% 0.29/0.46 => ( setbeta
% 0.29/0.46 => ( nonemptyE1
% 0.29/0.46 => ( nonemptyI
% 0.29/0.46 => ( nonemptyI1
% 0.29/0.46 => ( setadjoinIL
% 0.29/0.46 => ( emptyinunitempty
% 0.29/0.46 => ( setadjoinIR
% 0.29/0.46 => ( setadjoinE
% 0.29/0.46 => ( setadjoinOr
% 0.29/0.46 => ( setoftrueEq
% 0.29/0.46 => ( powersetI
% 0.29/0.46 => ( emptyinPowerset
% 0.29/0.46 => ( emptyInPowerset
% 0.29/0.46 => ( powersetE
% 0.29/0.46 => ( setunionI
% 0.29/0.46 => ( setunionE
% 0.29/0.46 => ( subPowSU
% 0.29/0.46 => ( exuE2
% 0.29/0.46 => ( nonemptyImpWitness
% 0.29/0.46 => ( uniqinunit
% 0.29/0.46 => ( notinsingleton
% 0.29/0.46 => ( eqinunit
% 0.29/0.46 => ( singletonsswitch
% 0.29/0.46 => ( upairsetE
% 0.29/0.46 => ( upairsetIL
% 0.29/0.46 => ( upairsetIR
% 0.29/0.46 => ( emptyE1
% 0.29/0.46 => ( vacuousDall
% 0.29/0.46 => ( quantDeMorgan1
% 0.29/0.46 => ( quantDeMorgan2
% 0.29/0.46 => ( quantDeMorgan3
% 0.29/0.46 => ( quantDeMorgan4
% 0.29/0.46 => ( prop2setI
% 0.29/0.46 => ( prop2set2propI
% 0.29/0.46 => ( notdexE
% 0.29/0.46 => ( notdallE
% 0.29/0.46 => ( exuI1
% 0.29/0.46 => ( exuI3
% 0.29/0.46 => ( exuI2
% 0.29/0.46 => ( inCongP
% 0.29/0.46 => ( in__Cong
% 0.29/0.46 => ( exuE3u
% 0.29/0.46 => ( exu__Cong
% 0.29/0.46 => ( emptyset__Cong
% 0.29/0.46 => ( setadjoin__Cong
% 0.29/0.46 => ( powerset__Cong
% 0.29/0.46 => ( setunion__Cong
% 0.29/0.46 => ( omega__Cong
% 0.29/0.46 => ( exuEu
% 0.29/0.46 => ( descr__Cong
% 0.29/0.46 => ( dsetconstr__Cong
% 0.29/0.46 => ( subsetI1
% 0.29/0.46 => ( eqimpsubset2
% 0.29/0.46 => ( eqimpsubset1
% 0.29/0.46 => ( subsetI2
% 0.29/0.46 => ( emptysetsubset
% 0.29/0.46 => ( subsetE
% 0.29/0.46 => ( subsetE2
% 0.29/0.46 => ( notsubsetI
% 0.29/0.46 => ( notequalI1
% 0.29/0.46 => ( notequalI2
% 0.29/0.46 => ( subsetRefl
% 0.29/0.46 => ( subsetTrans
% 0.29/0.46 => ( setadjoinSub
% 0.29/0.46 => ( setadjoinSub2
% 0.29/0.46 => ( subset2powerset
% 0.29/0.46 => ( setextsub
% 0.29/0.46 => ( subsetemptysetimpeq
% 0.29/0.46 => ( powersetI1
% 0.29/0.46 => ( powersetE1
% 0.29/0.46 => ( inPowerset
% 0.29/0.46 => ( powersetsubset
% 0.29/0.46 => ( sepInPowerset
% 0.29/0.46 => ( sepSubset
% 0.29/0.46 => ( binunionIL
% 0.29/0.46 => ( upairset2IR
% 0.29/0.46 => ( binunionIR
% 0.29/0.46 => ( binunionEcases
% 0.29/0.46 => ( binunionE
% 0.29/0.46 => ( binunionLsub
% 0.29/0.46 => ( binunionRsub
% 0.29/0.46 => ( binintersectI
% 0.29/0.46 => ( binintersectSubset5
% 0.29/0.46 => ( binintersectEL
% 0.29/0.46 => ( binintersectLsub
% 0.29/0.46 => ( binintersectSubset2
% 0.29/0.46 => ( binintersectSubset3
% 0.29/0.46 => ( binintersectER
% 0.29/0.46 => ( disjointsetsI1
% 0.29/0.46 => ( binintersectRsub
% 0.29/0.46 => ( binintersectSubset4
% 0.29/0.46 => ( binintersectSubset1
% 0.29/0.46 => ( bs114d
% 0.29/0.46 => ( setminusI
% 0.29/0.46 => ( setminusEL
% 0.29/0.46 => ( setminusER
% 0.29/0.46 => ( setminusSubset2
% 0.29/0.46 => ( setminusERneg
% 0.29/0.46 => ( setminusELneg
% 0.29/0.46 => ( setminusILneg
% 0.29/0.46 => ( setminusIRneg
% 0.29/0.46 => ( setminusLsub
% 0.29/0.46 => ( setminusSubset1
% 0.29/0.46 => ( symdiffE
% 0.29/0.46 => ( symdiffI1
% 0.29/0.46 => ( symdiffI2
% 0.29/0.46 => ( symdiffIneg1
% 0.29/0.46 => ( symdiffIneg2
% 0.29/0.46 => ( secondinupair
% 0.29/0.46 => ( setukpairIL
% 0.29/0.46 => ( setukpairIR
% 0.29/0.46 => ( kpairiskpair
% 0.29/0.46 => ( kpairp
% 0.29/0.46 => ( singletonsubset
% 0.29/0.46 => ( singletoninpowerset
% 0.29/0.46 => ( singletoninpowunion
% 0.29/0.46 => ( upairset2E
% 0.29/0.46 => ( upairsubunion
% 0.29/0.46 => ( upairinpowunion
% 0.29/0.46 => ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ B )
% 0.29/0.46 => ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 ------------------------
% 2.36/1.44 ---- Embedded in THF ---
% 2.36/1.44 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.36/1.44 %%% Generated on Tue Feb 24 12:28:58 EST 2026
% 2.36/1.44 %%% using '$$dhol' embedding, version 1.3.0.
% 2.36/1.44 %%% Logic specification used:
% 2.36/1.44 %%% thf(spec, logic, $$dhol).
% 2.36/1.44
% 2.36/1.44 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.EC9PjZGDVh/DTF2DTF12319.p
% See solution above
% 2.36/1.44 ------------------------
% 2.36/1.45 ---- Cleaned THF ---
% 2.36/1.45 thf(in_type,type,
% 2.36/1.45 in: $i > $i > $o ).
% 2.36/1.45
% 2.36/1.45 thf(exu_type,type,
% 2.36/1.45 exu: ( $i > $o ) > $o ).
% 2.36/1.45
% 2.36/1.45 thf(exu,definition,
% 2.36/1.45 ( exu
% 2.36/1.45 = ( ^ [Xphi: $i > $o] :
% 2.36/1.45 ? [Xx: $i] :
% 2.36/1.45 ( ( Xphi @ Xx )
% 2.36/1.45 & ! [Xy: $i] :
% 2.36/1.45 ( ( Xphi @ Xy )
% 2.36/1.45 => ( Xx = Xy ) ) ) ) ) ).
% 2.36/1.45
% 2.36/1.45 thf(setextAx_type,type,
% 2.36/1.45 setextAx: $o ).
% 2.36/1.45
% 2.36/1.45 thf(setextAx,definition,
% 2.36/1.45 ( setextAx
% 2.36/1.45 = ( ! [A: $i,B: $i] :
% 2.36/1.45 ( ! [Xx: $i] :
% 2.36/1.45 ( ( in @ Xx @ A )
% 2.36/1.45 <=> ( in @ Xx @ B ) )
% 2.36/1.45 => ( A = B ) ) ) ) ).
% 2.36/1.45
% 2.36/1.45 thf(emptyset_type,type,
% 2.36/1.45 emptyset: $i ).
% 2.36/1.45
% 2.36/1.45 thf(emptysetAx_type,type,
% 2.36/1.45 emptysetAx: $o ).
% 2.36/1.45
% 2.36/1.45 thf(emptysetAx,definition,
% 2.36/1.45 ( emptysetAx
% 2.36/1.45 = ( ! [Xx: $i] :
% 2.36/1.45 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.36/1.45
% 2.36/1.45 thf(setadjoin_type,type,
% 2.36/1.45 setadjoin: $i > $i > $i ).
% 2.36/1.45
% 2.36/1.45 thf(setadjoinAx_type,type,
% 2.36/1.45 setadjoinAx: $o ).
% 2.36/1.45
% 2.36/1.45 thf(setadjoinAx,definition,
% 2.36/1.45 ( setadjoinAx
% 2.36/1.45 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.36/1.45 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.36/1.45 <=> ( ( Xy = Xx )
% 2.36/1.45 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.36/1.45
% 2.36/1.45 thf(powerset_type,type,
% 2.36/1.45 powerset: $i > $i ).
% 2.36/1.45
% 2.36/1.45 thf(powersetAx_type,type,
% 2.36/1.45 powersetAx: $o ).
% 2.36/1.45
% 2.36/1.45 thf(powersetAx,definition,
% 2.36/1.45 ( powersetAx
% 2.36/1.45 = ( ! [A: $i,B: $i] :
% 2.36/1.45 ( ( in @ B @ ( powerset @ A ) )
% 2.36/1.45 <=> ! [Xx: $i] :
% 2.36/1.45 ( ( in @ Xx @ B )
% 2.36/1.45 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.36/1.45
% 2.36/1.45 thf(setunion_type,type,
% 2.36/1.45 setunion: $i > $i ).
% 2.36/1.45
% 2.36/1.45 thf(setunionAx_type,type,
% 2.36/1.45 setunionAx: $o ).
% 2.36/1.45
% 2.36/1.45 thf(setunionAx,definition,
% 2.36/1.45 ( setunionAx
% 2.36/1.45 = ( ! [A: $i,Xx: $i] :
% 2.36/1.45 ( ( in @ Xx @ ( setunion @ A ) )
% 2.36/1.45 <=> ? [B: $i] :
% 2.36/1.45 ( ( in @ Xx @ B )
% 2.36/1.45 & ( in @ B @ A ) ) ) ) ) ).
% 2.36/1.45
% 2.36/1.45 thf(omega_type,type,
% 2.36/1.45 omega: $i ).
% 2.36/1.45
% 2.36/1.45 thf(omega0Ax_type,type,
% 2.36/1.45 omega0Ax: $o ).
% 2.36/1.45
% 2.36/1.45 thf(omega0Ax,definition,
% 2.36/1.45 ( omega0Ax
% 2.36/1.45 = ( in @ emptyset @ omega ) ) ).
% 2.36/1.45
% 2.36/1.45 thf(omegaSAx_type,type,
% 2.36/1.45 omegaSAx: $o ).
% 2.36/1.45
% 2.36/1.45 thf(omegaSAx,definition,
% 2.36/1.45 ( omegaSAx
% 2.36/1.45 = ( ! [Xx: $i] :
% 2.36/1.45 ( ( in @ Xx @ omega )
% 2.36/1.45 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 2.36/1.45
% 2.36/1.45 thf(omegaIndAx_type,type,
% 2.36/1.45 omegaIndAx: $o ).
% 2.36/1.45
% 2.36/1.45 thf(omegaIndAx,definition,
% 2.36/1.45 ( omegaIndAx
% 2.36/1.45 = ( ! [A: $i] :
% 2.36/1.45 ( ( ( in @ emptyset @ A )
% 2.36/1.45 & ! [Xx: $i] :
% 2.36/1.45 ( ( ( in @ Xx @ omega )
% 2.36/1.45 & ( in @ Xx @ A ) )
% 2.36/1.45 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 2.36/1.45 => ! [Xx: $i] :
% 2.36/1.45 ( ( in @ Xx @ omega )
% 2.36/1.45 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.36/1.45
% 2.36/1.45 thf(replAx_type,type,
% 2.36/1.45 replAx: $o ).
% 2.36/1.45
% 2.36/1.45 thf(replAx,definition,
% 2.36/1.45 ( replAx
% 2.36/1.45 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 2.36/1.45 ( ! [Xx: $i] :
% 2.36/1.45 ( ( in @ Xx @ A )
% 2.36/1.45 => ( exu
% 2.36/1.45 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 2.36/1.45 => ? [B: $i] :
% 2.36/1.45 ! [Xx: $i] :
% 2.36/1.45 ( ( in @ Xx @ B )
% 2.36/1.45 <=> ? [Xy: $i] :
% 2.36/1.45 ( ( in @ Xy @ A )
% 2.36/1.45 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 2.36/1.45
% 2.36/1.45 thf(foundationAx_type,type,
% 2.36/1.45 foundationAx: $o ).
% 2.36/1.45
% 2.36/1.45 thf(foundationAx,definition,
% 2.36/1.45 ( foundationAx
% 2.36/1.45 = ( ! [A: $i] :
% 2.36/1.45 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.36/1.45 => ? [B: $i] :
% 2.36/1.45 ( ( in @ B @ A )
% 2.36/1.45 & ~ ? [Xx: $i] :
% 2.36/1.45 ( ( in @ Xx @ B )
% 2.36/1.45 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 2.36/1.45
% 2.36/1.45 thf(wellorderingAx_type,type,
% 2.36/1.45 wellorderingAx: $o ).
% 2.36/1.45
% 2.36/1.45 thf(wellorderingAx,definition,
% 2.36/1.45 ( wellorderingAx
% 2.36/1.45 = ( ! [A: $i] :
% 2.36/1.45 ? [B: $i] :
% 2.36/1.45 ( ! [C: $i] :
% 2.36/1.45 ( ( in @ C @ B )
% 2.36/1.45 => ! [Xx: $i] :
% 2.36/1.45 ( ( in @ Xx @ C )
% 2.36/1.45 => ( in @ Xx @ A ) ) )
% 2.36/1.45 & ! [Xx: $i,Xy: $i] :
% 2.36/1.45 ( ( ( in @ Xx @ A )
% 2.36/1.45 & ( in @ Xy @ A ) )
% 2.36/1.45 => ( ! [C: $i] :
% 2.36/1.45 ( ( in @ C @ B )
% 2.36/1.45 => ( ( in @ Xx @ C )
% 2.36/1.45 <=> ( in @ Xy @ C ) ) )
% 2.36/1.45 => ( Xx = Xy ) ) )
% 2.36/1.45 & ! [C: $i,D: $i] :
% 2.36/1.45 ( ( ( in @ C @ B )
% 2.36/1.45 & ( in @ D @ B ) )
% 2.36/1.45 => ( ! [Xx: $i] :
% 2.36/1.45 ( ( in @ Xx @ C )
% 2.36/1.45 => ( in @ Xx @ D ) )
% 2.36/1.45 | ! [Xx: $i] :
% 2.36/1.45 ( ( in @ Xx @ D )
% 2.36/1.45 => ( in @ Xx @ C ) ) ) )
% 2.36/1.45 & ! [C: $i] :
% 2.36/1.45 ( ( ! [Xx: $i] :
% 2.36/1.45 ( ( in @ Xx @ C )
% 2.36/1.45 => ( in @ Xx @ A ) )
% 2.36/1.45 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 2.36/1.45 => ? [D: $i,Xx: $i] :
% 2.36/1.45 ( ( in @ D @ B )
% 2.36/1.45 & ( in @ Xx @ C )
% 2.36/1.45 & ~ ? [Xy: $i] :
% 2.36/1.45 ( ( in @ Xy @ D )
% 2.36/1.45 & ( in @ Xy @ C ) )
% 2.36/1.45 & ! [E: $i] :
% 2.36/1.45 ( ( in @ E @ B )
% 2.36/1.45 => ( ! [Xy: $i] :
% 2.36/1.45 ( ( in @ Xy @ E )
% 2.36/1.45 => ( in @ Xy @ D ) )
% 2.36/1.45 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 2.36/1.45
% 2.36/1.45 thf(descr_type,type,
% 2.36/1.45 descr: ( $i > $o ) > $i ).
% 2.36/1.45
% 2.36/1.45 thf(descrp_type,type,
% 2.36/1.45 descrp: $o ).
% 2.36/1.45
% 2.36/1.45 thf(descrp,definition,
% 2.36/1.45 ( descrp
% 2.36/1.45 = ( ! [Xphi: $i > $o] :
% 2.36/1.45 ( ( exu
% 2.36/1.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.36/1.45 => ( Xphi
% 2.36/1.45 @ ( descr
% 2.36/1.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.36/1.45
% 2.36/1.45 thf(dsetconstr_type,type,
% 2.36/1.45 dsetconstr: $i > ( $i > $o ) > $i ).
% 2.36/1.45
% 2.36/1.45 thf(dsetconstrI_type,type,
% 2.36/1.45 dsetconstrI: $o ).
% 2.36/1.45
% 2.36/1.45 thf(dsetconstrI,definition,
% 2.36/1.45 ( dsetconstrI
% 2.36/1.45 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.36/1.45 ( ( in @ Xx @ A )
% 2.36/1.45 => ( ( Xphi @ Xx )
% 2.36/1.45 => ( in @ Xx
% 2.36/1.45 @ ( dsetconstr @ A
% 2.36/1.45 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.36/1.45
% 2.36/1.45 thf(dsetconstrEL_type,type,
% 2.36/1.45 dsetconstrEL: $o ).
% 2.36/1.45
% 2.36/1.45 thf(dsetconstrEL,definition,
% 2.36/1.45 ( dsetconstrEL
% 2.36/1.45 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.36/1.45 ( ( in @ Xx
% 2.36/1.45 @ ( dsetconstr @ A
% 2.36/1.45 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.36/1.45 => ( in @ Xx @ A ) ) ) ) ).
% 2.36/1.45
% 2.36/1.45 thf(dsetconstrER_type,type,
% 2.36/1.45 dsetconstrER: $o ).
% 2.36/1.45
% 2.36/1.45 thf(dsetconstrER,definition,
% 2.36/1.45 ( dsetconstrER
% 2.36/1.45 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.36/1.45 ( ( in @ Xx
% 2.36/1.45 @ ( dsetconstr @ A
% 2.36/1.45 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.36/1.45 => ( Xphi @ Xx ) ) ) ) ).
% 2.36/1.45
% 2.36/1.45 thf(exuE1_type,type,
% 2.36/1.45 exuE1: $o ).
% 2.36/1.45
% 2.36/1.45 thf(exuE1,definition,
% 2.36/1.45 ( exuE1
% 2.36/1.45 = ( ! [Xphi: $i > $o] :
% 2.36/1.45 ( ( exu
% 2.36/1.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.36/1.45 => ? [Xx: $i] :
% 2.36/1.45 ( ( Xphi @ Xx )
% 2.36/1.45 & ! [Xy: $i] :
% 2.36/1.45 ( ( Xphi @ Xy )
% 2.36/1.45 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.36/1.45
% 2.36/1.45 thf(prop2set_type,type,
% 2.36/1.45 prop2set: $o > $i ).
% 2.36/1.45
% 2.36/1.45 thf(prop2setE_type,type,
% 2.36/1.45 prop2setE: $o ).
% 2.36/1.45
% 2.36/1.45 thf(prop2setE,definition,
% 2.36/1.45 ( prop2setE
% 2.36/1.45 = ( ! [Xphi: $o,Xx: $i] :
% 2.36/1.45 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 2.36/1.45 => Xphi ) ) ) ).
% 2.36/1.45
% 2.36/1.45 thf(emptysetE_type,type,
% 2.36/1.45 emptysetE: $o ).
% 2.36/1.45
% 2.36/1.45 thf(emptysetE,definition,
% 2.36/1.45 ( emptysetE
% 2.36/1.45 = ( ! [Xx: $i] :
% 2.36/1.45 ( ( in @ Xx @ emptyset )
% 2.36/1.45 => ! [Xphi: $o] : Xphi ) ) ) ).
% 2.36/1.45
% 2.36/1.45 thf(emptysetimpfalse_type,type,
% 2.36/1.45 emptysetimpfalse: $o ).
% 2.36/1.45
% 2.36/1.45 thf(emptysetimpfalse,definition,
% 2.36/1.45 ( emptysetimpfalse
% 2.36/1.45 = ( ! [Xx: $i] :
% 2.36/1.45 ( ( in @ Xx @ emptyset )
% 2.36/1.45 => $false ) ) ) ).
% 2.36/1.45
% 2.36/1.45 thf(notinemptyset_type,type,
% 2.36/1.45 notinemptyset: $o ).
% 2.36/1.45
% 2.36/1.45 thf(notinemptyset,definition,
% 2.36/1.45 ( notinemptyset
% 2.36/1.45 = ( ! [Xx: $i] :
% 2.36/1.45 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.36/1.45
% 2.36/1.45 thf(exuE3e_type,type,
% 2.36/1.45 exuE3e: $o ).
% 2.36/1.45
% 2.36/1.45 thf(exuE3e,definition,
% 2.36/1.45 ( exuE3e
% 2.36/1.45 = ( ! [Xphi: $i > $o] :
% 2.36/1.45 ( ( exu
% 2.36/1.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.36/1.45 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 2.36/1.45
% 2.36/1.45 thf(setext_type,type,
% 2.36/1.45 setext: $o ).
% 2.36/1.45
% 2.36/1.45 thf(setext,definition,
% 2.36/1.45 ( setext
% 2.36/1.45 = ( ! [A: $i,B: $i] :
% 2.36/1.45 ( ! [Xx: $i] :
% 2.36/1.45 ( ( in @ Xx @ A )
% 2.36/1.45 => ( in @ Xx @ B ) )
% 2.36/1.45 => ( ! [Xx: $i] :
% 2.36/1.45 ( ( in @ Xx @ B )
% 2.36/1.45 => ( in @ Xx @ A ) )
% 2.36/1.45 => ( A = B ) ) ) ) ) ).
% 2.36/1.45
% 2.36/1.45 thf(emptyI_type,type,
% 2.36/1.45 emptyI: $o ).
% 2.36/1.45
% 2.36/1.45 thf(emptyI,definition,
% 2.36/1.45 ( emptyI
% 2.36/1.45 = ( ! [A: $i] :
% 2.36/1.45 ( ! [Xx: $i] :
% 2.36/1.45 ~ ( in @ Xx @ A )
% 2.36/1.45 => ( A = emptyset ) ) ) ) ).
% 2.36/1.45
% 2.36/1.45 thf(noeltsimpempty_type,type,
% 2.36/1.45 noeltsimpempty: $o ).
% 2.36/1.45
% 2.36/1.45 thf(noeltsimpempty,definition,
% 2.36/1.45 ( noeltsimpempty
% 2.36/1.45 = ( ! [A: $i] :
% 2.36/1.45 ( ! [Xx: $i] :
% 2.36/1.45 ~ ( in @ Xx @ A )
% 2.36/1.45 => ( A = emptyset ) ) ) ) ).
% 2.36/1.45
% 2.36/1.45 thf(setbeta_type,type,
% 2.36/1.45 setbeta: $o ).
% 2.36/1.46
% 2.36/1.46 thf(setbeta,definition,
% 2.36/1.46 ( setbeta
% 2.36/1.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.36/1.46 ( ( in @ Xx @ A )
% 2.36/1.46 => ( ( in @ Xx
% 2.36/1.46 @ ( dsetconstr @ A
% 2.36/1.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.36/1.46 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(nonempty_type,type,
% 2.36/1.46 nonempty: $i > $o ).
% 2.36/1.46
% 2.36/1.46 thf(nonempty,definition,
% 2.36/1.46 ( nonempty
% 2.36/1.46 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(nonemptyE1_type,type,
% 2.36/1.46 nonemptyE1: $o ).
% 2.36/1.46
% 2.36/1.46 thf(nonemptyE1,definition,
% 2.36/1.46 ( nonemptyE1
% 2.36/1.46 = ( ! [A: $i] :
% 2.36/1.46 ( ( nonempty @ A )
% 2.36/1.46 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(nonemptyI_type,type,
% 2.36/1.46 nonemptyI: $o ).
% 2.36/1.46
% 2.36/1.46 thf(nonemptyI,definition,
% 2.36/1.46 ( nonemptyI
% 2.36/1.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.36/1.46 ( ( in @ Xx @ A )
% 2.36/1.46 => ( ( Xphi @ Xx )
% 2.36/1.46 => ( nonempty
% 2.36/1.46 @ ( dsetconstr @ A
% 2.36/1.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(nonemptyI1_type,type,
% 2.36/1.46 nonemptyI1: $o ).
% 2.36/1.46
% 2.36/1.46 thf(nonemptyI1,definition,
% 2.36/1.46 ( nonemptyI1
% 2.36/1.46 = ( ! [A: $i] :
% 2.36/1.46 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.36/1.46 => ( nonempty @ A ) ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(setadjoinIL_type,type,
% 2.36/1.46 setadjoinIL: $o ).
% 2.36/1.46
% 2.36/1.46 thf(setadjoinIL,definition,
% 2.36/1.46 ( setadjoinIL
% 2.36/1.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(emptyinunitempty_type,type,
% 2.36/1.46 emptyinunitempty: $o ).
% 2.36/1.46
% 2.36/1.46 thf(emptyinunitempty,definition,
% 2.36/1.46 ( emptyinunitempty
% 2.36/1.46 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(setadjoinIR_type,type,
% 2.36/1.46 setadjoinIR: $o ).
% 2.36/1.46
% 2.36/1.46 thf(setadjoinIR,definition,
% 2.36/1.46 ( setadjoinIR
% 2.36/1.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.36/1.46 ( ( in @ Xy @ A )
% 2.36/1.46 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(setadjoinE_type,type,
% 2.36/1.46 setadjoinE: $o ).
% 2.36/1.46
% 2.36/1.46 thf(setadjoinE,definition,
% 2.36/1.46 ( setadjoinE
% 2.36/1.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.36/1.46 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.36/1.46 => ! [Xphi: $o] :
% 2.36/1.46 ( ( ( Xy = Xx )
% 2.36/1.46 => Xphi )
% 2.36/1.46 => ( ( ( in @ Xy @ A )
% 2.36/1.46 => Xphi )
% 2.36/1.46 => Xphi ) ) ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(setadjoinOr_type,type,
% 2.36/1.46 setadjoinOr: $o ).
% 2.36/1.46
% 2.36/1.46 thf(setadjoinOr,definition,
% 2.36/1.46 ( setadjoinOr
% 2.36/1.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.36/1.46 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.36/1.46 => ( ( Xy = Xx )
% 2.36/1.46 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(setoftrueEq_type,type,
% 2.36/1.46 setoftrueEq: $o ).
% 2.36/1.46
% 2.36/1.46 thf(setoftrueEq,definition,
% 2.36/1.46 ( setoftrueEq
% 2.36/1.46 = ( ! [A: $i] :
% 2.36/1.46 ( ( dsetconstr @ A
% 2.36/1.46 @ ^ [Xx: $i] : $true )
% 2.36/1.46 = A ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(powersetI_type,type,
% 2.36/1.46 powersetI: $o ).
% 2.36/1.46
% 2.36/1.46 thf(powersetI,definition,
% 2.36/1.46 ( powersetI
% 2.36/1.46 = ( ! [A: $i,B: $i] :
% 2.36/1.46 ( ! [Xx: $i] :
% 2.36/1.46 ( ( in @ Xx @ B )
% 2.36/1.46 => ( in @ Xx @ A ) )
% 2.36/1.46 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(emptyinPowerset_type,type,
% 2.36/1.46 emptyinPowerset: $o ).
% 2.36/1.46
% 2.36/1.46 thf(emptyinPowerset,definition,
% 2.36/1.46 ( emptyinPowerset
% 2.36/1.46 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(emptyInPowerset_type,type,
% 2.36/1.46 emptyInPowerset: $o ).
% 2.36/1.46
% 2.36/1.46 thf(emptyInPowerset,definition,
% 2.36/1.46 ( emptyInPowerset
% 2.36/1.46 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(powersetE_type,type,
% 2.36/1.46 powersetE: $o ).
% 2.36/1.46
% 2.36/1.46 thf(powersetE,definition,
% 2.36/1.46 ( powersetE
% 2.36/1.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.36/1.46 ( ( in @ B @ ( powerset @ A ) )
% 2.36/1.46 => ( ( in @ Xx @ B )
% 2.36/1.46 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(setunionI_type,type,
% 2.36/1.46 setunionI: $o ).
% 2.36/1.46
% 2.36/1.46 thf(setunionI,definition,
% 2.36/1.46 ( setunionI
% 2.36/1.46 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.36/1.46 ( ( in @ Xx @ B )
% 2.36/1.46 => ( ( in @ B @ A )
% 2.36/1.46 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(setunionE_type,type,
% 2.36/1.46 setunionE: $o ).
% 2.36/1.46
% 2.36/1.46 thf(setunionE,definition,
% 2.36/1.46 ( setunionE
% 2.36/1.46 = ( ! [A: $i,Xx: $i] :
% 2.36/1.46 ( ( in @ Xx @ ( setunion @ A ) )
% 2.36/1.46 => ! [Xphi: $o] :
% 2.36/1.46 ( ! [B: $i] :
% 2.36/1.46 ( ( in @ Xx @ B )
% 2.36/1.46 => ( ( in @ B @ A )
% 2.36/1.46 => Xphi ) )
% 2.36/1.46 => Xphi ) ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(subPowSU_type,type,
% 2.36/1.46 subPowSU: $o ).
% 2.36/1.46
% 2.36/1.46 thf(subPowSU,definition,
% 2.36/1.46 ( subPowSU
% 2.36/1.46 = ( ! [A: $i,Xx: $i] :
% 2.36/1.46 ( ( in @ Xx @ A )
% 2.36/1.46 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(exuE2_type,type,
% 2.36/1.46 exuE2: $o ).
% 2.36/1.46
% 2.36/1.46 thf(exuE2,definition,
% 2.36/1.46 ( exuE2
% 2.36/1.46 = ( ! [Xphi: $i > $o] :
% 2.36/1.46 ( ( exu
% 2.36/1.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.36/1.46 => ? [Xx: $i] :
% 2.36/1.46 ! [Xy: $i] :
% 2.36/1.46 ( ( Xphi @ Xy )
% 2.36/1.46 <=> ( Xy = Xx ) ) ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(nonemptyImpWitness_type,type,
% 2.36/1.46 nonemptyImpWitness: $o ).
% 2.36/1.46
% 2.36/1.46 thf(nonemptyImpWitness,definition,
% 2.36/1.46 ( nonemptyImpWitness
% 2.36/1.46 = ( ! [A: $i] :
% 2.36/1.46 ( ( nonempty @ A )
% 2.36/1.46 => ? [Xx: $i] :
% 2.36/1.46 ( ( in @ Xx @ A )
% 2.36/1.46 & $true ) ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(uniqinunit_type,type,
% 2.36/1.46 uniqinunit: $o ).
% 2.36/1.46
% 2.36/1.46 thf(uniqinunit,definition,
% 2.36/1.46 ( uniqinunit
% 2.36/1.46 = ( ! [Xx: $i,Xy: $i] :
% 2.36/1.46 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.36/1.46 => ( Xx = Xy ) ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(notinsingleton_type,type,
% 2.36/1.46 notinsingleton: $o ).
% 2.36/1.46
% 2.36/1.46 thf(notinsingleton,definition,
% 2.36/1.46 ( notinsingleton
% 2.36/1.46 = ( ! [Xx: $i,Xy: $i] :
% 2.36/1.46 ( ( Xx != Xy )
% 2.36/1.46 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(eqinunit_type,type,
% 2.36/1.46 eqinunit: $o ).
% 2.36/1.46
% 2.36/1.46 thf(eqinunit,definition,
% 2.36/1.46 ( eqinunit
% 2.36/1.46 = ( ! [Xx: $i,Xy: $i] :
% 2.36/1.46 ( ( Xx = Xy )
% 2.36/1.46 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(singletonsswitch_type,type,
% 2.36/1.46 singletonsswitch: $o ).
% 2.36/1.46
% 2.36/1.46 thf(singletonsswitch,definition,
% 2.36/1.46 ( singletonsswitch
% 2.36/1.46 = ( ! [Xx: $i,Xy: $i] :
% 2.36/1.46 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.36/1.46 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(upairsetE_type,type,
% 2.36/1.46 upairsetE: $o ).
% 2.36/1.46
% 2.36/1.46 thf(upairsetE,definition,
% 2.36/1.46 ( upairsetE
% 2.36/1.46 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.36/1.46 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 2.36/1.46 => ( ( Xz = Xx )
% 2.36/1.46 | ( Xz = Xy ) ) ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(upairsetIL_type,type,
% 2.36/1.46 upairsetIL: $o ).
% 2.36/1.46
% 2.36/1.46 thf(upairsetIL,definition,
% 2.36/1.46 ( upairsetIL
% 2.36/1.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(upairsetIR_type,type,
% 2.36/1.46 upairsetIR: $o ).
% 2.36/1.46
% 2.36/1.46 thf(upairsetIR,definition,
% 2.36/1.46 ( upairsetIR
% 2.36/1.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(emptyE1_type,type,
% 2.36/1.46 emptyE1: $o ).
% 2.36/1.46
% 2.36/1.46 thf(emptyE1,definition,
% 2.36/1.46 ( emptyE1
% 2.36/1.46 = ( ! [A: $i,Xphi: $i > $o] :
% 2.36/1.46 ( ? [Xx: $i] :
% 2.36/1.46 ( ( in @ Xx @ A )
% 2.36/1.46 & ( Xphi @ Xx ) )
% 2.36/1.46 => ( ( ( dsetconstr @ A
% 2.36/1.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.36/1.46 = emptyset )
% 2.36/1.46 => $false ) ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(vacuousDall_type,type,
% 2.36/1.46 vacuousDall: $o ).
% 2.36/1.46
% 2.36/1.46 thf(vacuousDall,definition,
% 2.36/1.46 ( vacuousDall
% 2.36/1.46 = ( ! [Xphi: $i > $o,Xx: $i] :
% 2.36/1.46 ( ( in @ Xx @ emptyset )
% 2.36/1.46 => ( Xphi @ Xx ) ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(quantDeMorgan1_type,type,
% 2.36/1.46 quantDeMorgan1: $o ).
% 2.36/1.46
% 2.36/1.46 thf(quantDeMorgan1,definition,
% 2.36/1.46 ( quantDeMorgan1
% 2.36/1.46 = ( ! [A: $i,Xphi: $i > $o] :
% 2.36/1.46 ( ~ ! [Xx: $i] :
% 2.36/1.46 ( ( in @ Xx @ A )
% 2.36/1.46 => ( Xphi @ Xx ) )
% 2.36/1.46 => ? [Xx: $i] :
% 2.36/1.46 ( ( in @ Xx @ A )
% 2.36/1.46 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(quantDeMorgan2_type,type,
% 2.36/1.46 quantDeMorgan2: $o ).
% 2.36/1.46
% 2.36/1.46 thf(quantDeMorgan2,definition,
% 2.36/1.46 ( quantDeMorgan2
% 2.36/1.46 = ( ! [A: $i,Xphi: $i > $o] :
% 2.36/1.46 ( ! [Xx: $i] :
% 2.36/1.46 ( ( in @ Xx @ A )
% 2.36/1.46 => ~ ( Xphi @ Xx ) )
% 2.36/1.46 => ~ ? [Xx: $i] :
% 2.36/1.46 ( ( in @ Xx @ A )
% 2.36/1.46 & ( Xphi @ Xx ) ) ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(quantDeMorgan3_type,type,
% 2.36/1.46 quantDeMorgan3: $o ).
% 2.36/1.46
% 2.36/1.46 thf(quantDeMorgan3,definition,
% 2.36/1.46 ( quantDeMorgan3
% 2.36/1.46 = ( ! [A: $i,Xphi: $i > $o] :
% 2.36/1.46 ( ~ ? [Xx: $i] :
% 2.36/1.46 ( ( in @ Xx @ A )
% 2.36/1.46 & ( Xphi @ Xx ) )
% 2.36/1.46 => ! [Xx: $i] :
% 2.36/1.46 ( ( in @ Xx @ A )
% 2.36/1.46 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(quantDeMorgan4_type,type,
% 2.36/1.46 quantDeMorgan4: $o ).
% 2.36/1.46
% 2.36/1.46 thf(quantDeMorgan4,definition,
% 2.36/1.46 ( quantDeMorgan4
% 2.36/1.46 = ( ! [A: $i,Xphi: $i > $o] :
% 2.36/1.46 ( ? [Xx: $i] :
% 2.36/1.46 ( ( in @ Xx @ A )
% 2.36/1.46 & ~ ( Xphi @ Xx ) )
% 2.36/1.46 => ~ ! [Xx: $i] :
% 2.36/1.46 ( ( in @ Xx @ A )
% 2.36/1.46 => ( Xphi @ Xx ) ) ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(prop2setI_type,type,
% 2.36/1.46 prop2setI: $o ).
% 2.36/1.46
% 2.36/1.46 thf(prop2setI,definition,
% 2.36/1.46 ( prop2setI
% 2.36/1.46 = ( ! [Xphi: $o] :
% 2.36/1.46 ( Xphi
% 2.36/1.46 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(set2prop_type,type,
% 2.36/1.46 set2prop: $i > $o ).
% 2.36/1.46
% 2.36/1.46 thf(prop2set2propI_type,type,
% 2.36/1.46 prop2set2propI: $o ).
% 2.36/1.46
% 2.36/1.46 thf(prop2set2propI,definition,
% 2.36/1.46 ( prop2set2propI
% 2.36/1.46 = ( ! [Xphi: $o] :
% 2.36/1.46 ( Xphi
% 2.36/1.46 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(notdexE_type,type,
% 2.36/1.46 notdexE: $o ).
% 2.36/1.46
% 2.36/1.46 thf(notdexE,definition,
% 2.36/1.46 ( notdexE
% 2.36/1.46 = ( ! [A: $i,Xphi: $i > $o] :
% 2.36/1.46 ( ~ ? [Xx: $i] :
% 2.36/1.46 ( ( in @ Xx @ A )
% 2.36/1.46 & ( Xphi @ Xx ) )
% 2.36/1.46 => ! [Xx: $i] :
% 2.36/1.46 ( ( in @ Xx @ A )
% 2.36/1.46 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(notdallE_type,type,
% 2.36/1.46 notdallE: $o ).
% 2.36/1.46
% 2.36/1.46 thf(notdallE,definition,
% 2.36/1.46 ( notdallE
% 2.36/1.46 = ( ! [A: $i,Xphi: $i > $o] :
% 2.36/1.46 ( ~ ! [Xx: $i] :
% 2.36/1.46 ( ( in @ Xx @ A )
% 2.36/1.46 => ( Xphi @ Xx ) )
% 2.36/1.46 => ? [Xx: $i] :
% 2.36/1.46 ( ( in @ Xx @ A )
% 2.36/1.46 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(exuI1_type,type,
% 2.36/1.46 exuI1: $o ).
% 2.36/1.46
% 2.36/1.46 thf(exuI1,definition,
% 2.36/1.46 ( exuI1
% 2.36/1.46 = ( ! [Xphi: $i > $o] :
% 2.36/1.46 ( ? [Xx: $i] :
% 2.36/1.46 ( ( Xphi @ Xx )
% 2.36/1.46 & ! [Xy: $i] :
% 2.36/1.46 ( ( Xphi @ Xy )
% 2.36/1.46 => ( Xx = Xy ) ) )
% 2.36/1.46 => ( exu
% 2.36/1.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(exuI3_type,type,
% 2.36/1.46 exuI3: $o ).
% 2.36/1.46
% 2.36/1.46 thf(exuI3,definition,
% 2.36/1.46 ( exuI3
% 2.36/1.46 = ( ! [Xphi: $i > $o] :
% 2.36/1.46 ( ? [Xx: $i] : ( Xphi @ Xx )
% 2.36/1.46 => ( ! [Xx: $i,Xy: $i] :
% 2.36/1.46 ( ( Xphi @ Xx )
% 2.36/1.46 => ( ( Xphi @ Xy )
% 2.36/1.46 => ( Xx = Xy ) ) )
% 2.36/1.46 => ( exu
% 2.36/1.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(exuI2_type,type,
% 2.36/1.46 exuI2: $o ).
% 2.36/1.46
% 2.36/1.46 thf(exuI2,definition,
% 2.36/1.46 ( exuI2
% 2.36/1.46 = ( ! [Xphi: $i > $o] :
% 2.36/1.46 ( ? [Xx: $i] :
% 2.36/1.46 ! [Xy: $i] :
% 2.36/1.46 ( ( Xphi @ Xy )
% 2.36/1.46 <=> ( Xy = Xx ) )
% 2.36/1.46 => ( exu
% 2.36/1.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(inCongP_type,type,
% 2.36/1.46 inCongP: $o ).
% 2.36/1.46
% 2.36/1.46 thf(inCongP,definition,
% 2.36/1.46 ( inCongP
% 2.36/1.46 = ( ! [A: $i,B: $i] :
% 2.36/1.46 ( ( A = B )
% 2.36/1.46 => ! [Xx: $i,Xy: $i] :
% 2.36/1.46 ( ( Xx = Xy )
% 2.36/1.46 => ( ( in @ Xx @ A )
% 2.36/1.46 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(in__Cong_type,type,
% 2.36/1.46 in__Cong: $o ).
% 2.36/1.46
% 2.36/1.46 thf(in__Cong,definition,
% 2.36/1.46 ( in__Cong
% 2.36/1.46 = ( ! [A: $i,B: $i] :
% 2.36/1.46 ( ( A = B )
% 2.36/1.46 => ! [Xx: $i,Xy: $i] :
% 2.36/1.46 ( ( Xx = Xy )
% 2.36/1.46 => ( ( in @ Xx @ A )
% 2.36/1.46 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(exuE3u_type,type,
% 2.36/1.46 exuE3u: $o ).
% 2.36/1.46
% 2.36/1.46 thf(exuE3u,definition,
% 2.36/1.46 ( exuE3u
% 2.36/1.46 = ( ! [Xphi: $i > $o] :
% 2.36/1.46 ( ( exu
% 2.36/1.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.36/1.46 => ! [Xx: $i,Xy: $i] :
% 2.36/1.46 ( ( Xphi @ Xx )
% 2.36/1.46 => ( ( Xphi @ Xy )
% 2.36/1.46 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(exu__Cong_type,type,
% 2.36/1.46 exu__Cong: $o ).
% 2.36/1.46
% 2.36/1.46 thf(exu__Cong,definition,
% 2.36/1.46 ( exu__Cong
% 2.36/1.46 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.36/1.46 ( ! [Xx: $i,Xy: $i] :
% 2.36/1.46 ( ( Xx = Xy )
% 2.36/1.46 => ( ( Xphi @ Xx )
% 2.36/1.46 <=> ( Xpsi @ Xy ) ) )
% 2.36/1.46 => ( ( exu
% 2.36/1.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.36/1.46 <=> ( exu
% 2.36/1.46 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(emptyset__Cong_type,type,
% 2.36/1.46 emptyset__Cong: $o ).
% 2.36/1.46
% 2.36/1.46 thf(emptyset__Cong,definition,
% 2.36/1.46 ( emptyset__Cong
% 2.36/1.46 = ( emptyset = emptyset ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(setadjoin__Cong_type,type,
% 2.36/1.46 setadjoin__Cong: $o ).
% 2.36/1.46
% 2.36/1.46 thf(setadjoin__Cong,definition,
% 2.36/1.46 ( setadjoin__Cong
% 2.36/1.46 = ( ! [Xx: $i,Xy: $i] :
% 2.36/1.46 ( ( Xx = Xy )
% 2.36/1.46 => ! [Xz: $i,Xu: $i] :
% 2.36/1.46 ( ( Xz = Xu )
% 2.36/1.46 => ( ( setadjoin @ Xx @ Xz )
% 2.36/1.46 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(powerset__Cong_type,type,
% 2.36/1.46 powerset__Cong: $o ).
% 2.36/1.46
% 2.36/1.46 thf(powerset__Cong,definition,
% 2.36/1.46 ( powerset__Cong
% 2.36/1.46 = ( ! [A: $i,B: $i] :
% 2.36/1.46 ( ( A = B )
% 2.36/1.46 => ( ( powerset @ A )
% 2.36/1.46 = ( powerset @ B ) ) ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(setunion__Cong_type,type,
% 2.36/1.46 setunion__Cong: $o ).
% 2.36/1.46
% 2.36/1.46 thf(setunion__Cong,definition,
% 2.36/1.46 ( setunion__Cong
% 2.36/1.46 = ( ! [A: $i,B: $i] :
% 2.36/1.46 ( ( A = B )
% 2.36/1.46 => ( ( setunion @ A )
% 2.36/1.46 = ( setunion @ B ) ) ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(omega__Cong_type,type,
% 2.36/1.46 omega__Cong: $o ).
% 2.36/1.46
% 2.36/1.46 thf(omega__Cong,definition,
% 2.36/1.46 ( omega__Cong
% 2.36/1.46 = ( omega = omega ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(exuEu_type,type,
% 2.36/1.46 exuEu: $o ).
% 2.36/1.46
% 2.36/1.46 thf(exuEu,definition,
% 2.36/1.46 ( exuEu
% 2.36/1.46 = ( ! [Xphi: $i > $o] :
% 2.36/1.46 ( ( exu
% 2.36/1.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.36/1.46 => ! [Xx: $i,Xy: $i] :
% 2.36/1.46 ( ( Xphi @ Xx )
% 2.36/1.46 => ( ( Xphi @ Xy )
% 2.36/1.46 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(descr__Cong_type,type,
% 2.36/1.46 descr__Cong: $o ).
% 2.36/1.46
% 2.36/1.46 thf(descr__Cong,definition,
% 2.36/1.46 ( descr__Cong
% 2.36/1.46 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.36/1.46 ( ! [Xx: $i,Xy: $i] :
% 2.36/1.46 ( ( Xx = Xy )
% 2.36/1.46 => ( ( Xphi @ Xx )
% 2.36/1.46 <=> ( Xpsi @ Xy ) ) )
% 2.36/1.46 => ( ( exu
% 2.36/1.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.36/1.46 => ( ( exu
% 2.36/1.46 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 2.36/1.46 => ( ( descr
% 2.36/1.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.36/1.46 = ( descr
% 2.36/1.46 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(dsetconstr__Cong_type,type,
% 2.36/1.46 dsetconstr__Cong: $o ).
% 2.36/1.46
% 2.36/1.46 thf(dsetconstr__Cong,definition,
% 2.36/1.46 ( dsetconstr__Cong
% 2.36/1.46 = ( ! [A: $i,B: $i] :
% 2.36/1.46 ( ( A = B )
% 2.36/1.46 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.36/1.46 ( ! [Xx: $i] :
% 2.36/1.46 ( ( in @ Xx @ A )
% 2.36/1.46 => ! [Xy: $i] :
% 2.36/1.46 ( ( in @ Xy @ B )
% 2.36/1.46 => ( ( Xx = Xy )
% 2.36/1.46 => ( ( Xphi @ Xx )
% 2.36/1.46 <=> ( Xpsi @ Xy ) ) ) ) )
% 2.36/1.46 => ( ( dsetconstr @ A
% 2.36/1.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.36/1.46 = ( dsetconstr @ B
% 2.36/1.46 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(subset_type,type,
% 2.36/1.46 subset: $i > $i > $o ).
% 2.36/1.46
% 2.36/1.46 thf(disjoint_type,type,
% 2.36/1.46 disjoint: $i > $i > $o ).
% 2.36/1.46
% 2.36/1.46 thf(setsmeet_type,type,
% 2.36/1.46 setsmeet: $i > $i > $o ).
% 2.36/1.46
% 2.36/1.46 thf(subsetI1_type,type,
% 2.36/1.46 subsetI1: $o ).
% 2.36/1.46
% 2.36/1.46 thf(subsetI1,definition,
% 2.36/1.46 ( subsetI1
% 2.36/1.46 = ( ! [A: $i,B: $i] :
% 2.36/1.46 ( ! [Xx: $i] :
% 2.36/1.46 ( ( in @ Xx @ A )
% 2.36/1.46 => ( in @ Xx @ B ) )
% 2.36/1.46 => ( subset @ A @ B ) ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(eqimpsubset2_type,type,
% 2.36/1.46 eqimpsubset2: $o ).
% 2.36/1.46
% 2.36/1.46 thf(eqimpsubset2,definition,
% 2.36/1.46 ( eqimpsubset2
% 2.36/1.46 = ( ! [A: $i,B: $i] :
% 2.36/1.46 ( ( A = B )
% 2.36/1.46 => ( subset @ B @ A ) ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(eqimpsubset1_type,type,
% 2.36/1.46 eqimpsubset1: $o ).
% 2.36/1.46
% 2.36/1.46 thf(eqimpsubset1,definition,
% 2.36/1.46 ( eqimpsubset1
% 2.36/1.46 = ( ! [A: $i,B: $i] :
% 2.36/1.46 ( ( A = B )
% 2.36/1.46 => ( subset @ A @ B ) ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(subsetI2_type,type,
% 2.36/1.46 subsetI2: $o ).
% 2.36/1.46
% 2.36/1.46 thf(subsetI2,definition,
% 2.36/1.46 ( subsetI2
% 2.36/1.46 = ( ! [A: $i,B: $i] :
% 2.36/1.46 ( ! [Xx: $i] :
% 2.36/1.46 ( ( in @ Xx @ A )
% 2.36/1.46 => ( in @ Xx @ B ) )
% 2.36/1.46 => ( subset @ A @ B ) ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(emptysetsubset_type,type,
% 2.36/1.46 emptysetsubset: $o ).
% 2.36/1.46
% 2.36/1.46 thf(emptysetsubset,definition,
% 2.36/1.46 ( emptysetsubset
% 2.36/1.46 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(subsetE_type,type,
% 2.36/1.46 subsetE: $o ).
% 2.36/1.46
% 2.36/1.46 thf(subsetE,definition,
% 2.36/1.46 ( subsetE
% 2.36/1.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.36/1.46 ( ( subset @ A @ B )
% 2.36/1.46 => ( ( in @ Xx @ A )
% 2.36/1.46 => ( in @ Xx @ B ) ) ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(subsetE2_type,type,
% 2.36/1.46 subsetE2: $o ).
% 2.36/1.46
% 2.36/1.46 thf(subsetE2,definition,
% 2.36/1.46 ( subsetE2
% 2.36/1.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.36/1.46 ( ( subset @ A @ B )
% 2.36/1.46 => ( ~ ( in @ Xx @ B )
% 2.36/1.46 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(notsubsetI_type,type,
% 2.36/1.46 notsubsetI: $o ).
% 2.36/1.46
% 2.36/1.46 thf(notsubsetI,definition,
% 2.36/1.46 ( notsubsetI
% 2.36/1.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.36/1.46 ( ( in @ Xx @ A )
% 2.36/1.46 => ( ~ ( in @ Xx @ B )
% 2.36/1.46 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(notequalI1_type,type,
% 2.36/1.46 notequalI1: $o ).
% 2.36/1.46
% 2.36/1.46 thf(notequalI1,definition,
% 2.36/1.46 ( notequalI1
% 2.36/1.46 = ( ! [A: $i,B: $i] :
% 2.36/1.46 ( ~ ( subset @ A @ B )
% 2.36/1.46 => ( A != B ) ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(notequalI2_type,type,
% 2.36/1.46 notequalI2: $o ).
% 2.36/1.46
% 2.36/1.46 thf(notequalI2,definition,
% 2.36/1.46 ( notequalI2
% 2.36/1.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.36/1.46 ( ( in @ Xx @ A )
% 2.36/1.46 => ( ~ ( in @ Xx @ B )
% 2.36/1.46 => ( A != B ) ) ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(subsetRefl_type,type,
% 2.36/1.46 subsetRefl: $o ).
% 2.36/1.46
% 2.36/1.46 thf(subsetRefl,definition,
% 2.36/1.46 ( subsetRefl
% 2.36/1.46 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(subsetTrans_type,type,
% 2.36/1.46 subsetTrans: $o ).
% 2.36/1.46
% 2.36/1.46 thf(subsetTrans,definition,
% 2.36/1.46 ( subsetTrans
% 2.36/1.46 = ( ! [A: $i,B: $i,C: $i] :
% 2.36/1.46 ( ( subset @ A @ B )
% 2.36/1.46 => ( ( subset @ B @ C )
% 2.36/1.46 => ( subset @ A @ C ) ) ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(setadjoinSub_type,type,
% 2.36/1.46 setadjoinSub: $o ).
% 2.36/1.46
% 2.36/1.46 thf(setadjoinSub,definition,
% 2.36/1.46 ( setadjoinSub
% 2.36/1.46 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(setadjoinSub2_type,type,
% 2.36/1.46 setadjoinSub2: $o ).
% 2.36/1.46
% 2.36/1.46 thf(setadjoinSub2,definition,
% 2.36/1.46 ( setadjoinSub2
% 2.36/1.46 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.36/1.46 ( ( subset @ A @ B )
% 2.36/1.46 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(subset2powerset_type,type,
% 2.36/1.46 subset2powerset: $o ).
% 2.36/1.46
% 2.36/1.46 thf(subset2powerset,definition,
% 2.36/1.46 ( subset2powerset
% 2.36/1.46 = ( ! [A: $i,B: $i] :
% 2.36/1.46 ( ( subset @ A @ B )
% 2.36/1.46 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(setextsub_type,type,
% 2.36/1.46 setextsub: $o ).
% 2.36/1.46
% 2.36/1.46 thf(setextsub,definition,
% 2.36/1.46 ( setextsub
% 2.36/1.46 = ( ! [A: $i,B: $i] :
% 2.36/1.46 ( ( subset @ A @ B )
% 2.36/1.46 => ( ( subset @ B @ A )
% 2.36/1.46 => ( A = B ) ) ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(subsetemptysetimpeq_type,type,
% 2.36/1.46 subsetemptysetimpeq: $o ).
% 2.36/1.46
% 2.36/1.46 thf(subsetemptysetimpeq,definition,
% 2.36/1.46 ( subsetemptysetimpeq
% 2.36/1.46 = ( ! [A: $i] :
% 2.36/1.46 ( ( subset @ A @ emptyset )
% 2.36/1.46 => ( A = emptyset ) ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(powersetI1_type,type,
% 2.36/1.46 powersetI1: $o ).
% 2.36/1.46
% 2.36/1.46 thf(powersetI1,definition,
% 2.36/1.46 ( powersetI1
% 2.36/1.46 = ( ! [A: $i,B: $i] :
% 2.36/1.46 ( ( subset @ B @ A )
% 2.36/1.46 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(powersetE1_type,type,
% 2.36/1.46 powersetE1: $o ).
% 2.36/1.46
% 2.36/1.46 thf(powersetE1,definition,
% 2.36/1.46 ( powersetE1
% 2.36/1.46 = ( ! [A: $i,B: $i] :
% 2.36/1.46 ( ( in @ B @ ( powerset @ A ) )
% 2.36/1.46 => ( subset @ B @ A ) ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(inPowerset_type,type,
% 2.36/1.46 inPowerset: $o ).
% 2.36/1.46
% 2.36/1.46 thf(inPowerset,definition,
% 2.36/1.46 ( inPowerset
% 2.36/1.46 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(powersetsubset_type,type,
% 2.36/1.46 powersetsubset: $o ).
% 2.36/1.46
% 2.36/1.46 thf(powersetsubset,definition,
% 2.36/1.46 ( powersetsubset
% 2.36/1.46 = ( ! [A: $i,B: $i] :
% 2.36/1.46 ( ( subset @ A @ B )
% 2.36/1.46 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(sepInPowerset_type,type,
% 2.36/1.46 sepInPowerset: $o ).
% 2.36/1.46
% 2.36/1.46 thf(sepInPowerset,definition,
% 2.36/1.46 ( sepInPowerset
% 2.36/1.46 = ( ! [A: $i,Xphi: $i > $o] :
% 2.36/1.46 ( in
% 2.36/1.46 @ ( dsetconstr @ A
% 2.36/1.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.36/1.46 @ ( powerset @ A ) ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(sepSubset_type,type,
% 2.36/1.46 sepSubset: $o ).
% 2.36/1.46
% 2.36/1.46 thf(sepSubset,definition,
% 2.36/1.46 ( sepSubset
% 2.36/1.46 = ( ! [A: $i,Xphi: $i > $o] :
% 2.36/1.46 ( subset
% 2.36/1.46 @ ( dsetconstr @ A
% 2.36/1.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.36/1.46 @ A ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(binunion_type,type,
% 2.36/1.46 binunion: $i > $i > $i ).
% 2.36/1.46
% 2.36/1.46 thf(binunionIL_type,type,
% 2.36/1.46 binunionIL: $o ).
% 2.36/1.46
% 2.36/1.46 thf(binunionIL,definition,
% 2.36/1.46 ( binunionIL
% 2.36/1.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.36/1.46 ( ( in @ Xx @ A )
% 2.36/1.46 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(upairset2IR_type,type,
% 2.36/1.46 upairset2IR: $o ).
% 2.36/1.46
% 2.36/1.46 thf(upairset2IR,definition,
% 2.36/1.46 ( upairset2IR
% 2.36/1.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(binunionIR_type,type,
% 2.36/1.46 binunionIR: $o ).
% 2.36/1.46
% 2.36/1.46 thf(binunionIR,definition,
% 2.36/1.46 ( binunionIR
% 2.36/1.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.36/1.46 ( ( in @ Xx @ B )
% 2.36/1.46 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(binunionEcases_type,type,
% 2.36/1.46 binunionEcases: $o ).
% 2.36/1.46
% 2.36/1.46 thf(binunionEcases,definition,
% 2.36/1.46 ( binunionEcases
% 2.36/1.46 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 2.36/1.46 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 2.36/1.46 => ( ( ( in @ Xx @ A )
% 2.36/1.46 => Xphi )
% 2.36/1.46 => ( ( ( in @ Xx @ B )
% 2.36/1.46 => Xphi )
% 2.36/1.46 => Xphi ) ) ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(binunionE_type,type,
% 2.36/1.46 binunionE: $o ).
% 2.36/1.46
% 2.36/1.46 thf(binunionE,definition,
% 2.36/1.46 ( binunionE
% 2.36/1.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.36/1.46 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 2.36/1.46 => ( ( in @ Xx @ A )
% 2.36/1.46 | ( in @ Xx @ B ) ) ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(binunionLsub_type,type,
% 2.36/1.46 binunionLsub: $o ).
% 2.36/1.46
% 2.36/1.46 thf(binunionLsub,definition,
% 2.36/1.46 ( binunionLsub
% 2.36/1.46 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(binunionRsub_type,type,
% 2.36/1.46 binunionRsub: $o ).
% 2.36/1.46
% 2.36/1.46 thf(binunionRsub,definition,
% 2.36/1.46 ( binunionRsub
% 2.36/1.46 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(binintersect_type,type,
% 2.36/1.46 binintersect: $i > $i > $i ).
% 2.36/1.46
% 2.36/1.46 thf(binintersectI_type,type,
% 2.36/1.46 binintersectI: $o ).
% 2.36/1.46
% 2.36/1.46 thf(binintersectI,definition,
% 2.36/1.46 ( binintersectI
% 2.36/1.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.36/1.46 ( ( in @ Xx @ A )
% 2.36/1.46 => ( ( in @ Xx @ B )
% 2.36/1.46 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(binintersectSubset5_type,type,
% 2.36/1.46 binintersectSubset5: $o ).
% 2.36/1.46
% 2.36/1.46 thf(binintersectSubset5,definition,
% 2.36/1.46 ( binintersectSubset5
% 2.36/1.46 = ( ! [A: $i,B: $i,C: $i] :
% 2.36/1.46 ( ( subset @ C @ A )
% 2.36/1.46 => ( ( subset @ C @ B )
% 2.36/1.46 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(binintersectEL_type,type,
% 2.36/1.46 binintersectEL: $o ).
% 2.36/1.46
% 2.36/1.46 thf(binintersectEL,definition,
% 2.36/1.46 ( binintersectEL
% 2.36/1.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.36/1.46 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 2.36/1.46 => ( in @ Xx @ A ) ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(binintersectLsub_type,type,
% 2.36/1.46 binintersectLsub: $o ).
% 2.36/1.46
% 2.36/1.46 thf(binintersectLsub,definition,
% 2.36/1.46 ( binintersectLsub
% 2.36/1.46 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(binintersectSubset2_type,type,
% 2.36/1.46 binintersectSubset2: $o ).
% 2.36/1.46
% 2.36/1.46 thf(binintersectSubset2,definition,
% 2.36/1.46 ( binintersectSubset2
% 2.36/1.46 = ( ! [A: $i,B: $i] :
% 2.36/1.46 ( ( subset @ A @ B )
% 2.36/1.46 => ( ( binintersect @ A @ B )
% 2.36/1.46 = A ) ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(binintersectSubset3_type,type,
% 2.36/1.46 binintersectSubset3: $o ).
% 2.36/1.46
% 2.36/1.46 thf(binintersectSubset3,definition,
% 2.36/1.46 ( binintersectSubset3
% 2.36/1.46 = ( ! [A: $i,B: $i] :
% 2.36/1.46 ( ( ( binintersect @ A @ B )
% 2.36/1.46 = B )
% 2.36/1.46 => ( subset @ B @ A ) ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(binintersectER_type,type,
% 2.36/1.46 binintersectER: $o ).
% 2.36/1.46
% 2.36/1.46 thf(binintersectER,definition,
% 2.36/1.46 ( binintersectER
% 2.36/1.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.36/1.46 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 2.36/1.46 => ( in @ Xx @ B ) ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(disjointsetsI1_type,type,
% 2.36/1.46 disjointsetsI1: $o ).
% 2.36/1.46
% 2.36/1.46 thf(disjointsetsI1,definition,
% 2.36/1.46 ( disjointsetsI1
% 2.36/1.46 = ( ! [A: $i,B: $i] :
% 2.36/1.46 ( ~ ? [Xx: $i] :
% 2.36/1.46 ( ( in @ Xx @ A )
% 2.36/1.46 & ( in @ Xx @ B ) )
% 2.36/1.46 => ( ( binintersect @ A @ B )
% 2.36/1.46 = emptyset ) ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(binintersectRsub_type,type,
% 2.36/1.46 binintersectRsub: $o ).
% 2.36/1.46
% 2.36/1.46 thf(binintersectRsub,definition,
% 2.36/1.46 ( binintersectRsub
% 2.36/1.46 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(binintersectSubset4_type,type,
% 2.36/1.46 binintersectSubset4: $o ).
% 2.36/1.46
% 2.36/1.46 thf(binintersectSubset4,definition,
% 2.36/1.46 ( binintersectSubset4
% 2.36/1.46 = ( ! [A: $i,B: $i] :
% 2.36/1.46 ( ( subset @ B @ A )
% 2.36/1.46 => ( ( binintersect @ A @ B )
% 2.36/1.46 = B ) ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(binintersectSubset1_type,type,
% 2.36/1.46 binintersectSubset1: $o ).
% 2.36/1.46
% 2.36/1.46 thf(binintersectSubset1,definition,
% 2.36/1.46 ( binintersectSubset1
% 2.36/1.46 = ( ! [A: $i,B: $i] :
% 2.36/1.46 ( ( ( binintersect @ A @ B )
% 2.36/1.46 = A )
% 2.36/1.46 => ( subset @ A @ B ) ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(bs114d_type,type,
% 2.36/1.46 bs114d: $o ).
% 2.36/1.46
% 2.36/1.46 thf(bs114d,definition,
% 2.36/1.46 ( bs114d
% 2.36/1.46 = ( ! [A: $i,B: $i,C: $i] :
% 2.36/1.46 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 2.36/1.46 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(regular_type,type,
% 2.36/1.46 regular: $i > $o ).
% 2.36/1.46
% 2.36/1.46 thf(setminus_type,type,
% 2.36/1.46 setminus: $i > $i > $i ).
% 2.36/1.46
% 2.36/1.46 thf(setminusI_type,type,
% 2.36/1.46 setminusI: $o ).
% 2.36/1.46
% 2.36/1.46 thf(setminusI,definition,
% 2.36/1.46 ( setminusI
% 2.36/1.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.36/1.46 ( ( in @ Xx @ A )
% 2.36/1.46 => ( ~ ( in @ Xx @ B )
% 2.36/1.46 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(setminusEL_type,type,
% 2.36/1.46 setminusEL: $o ).
% 2.36/1.46
% 2.36/1.46 thf(setminusEL,definition,
% 2.36/1.46 ( setminusEL
% 2.36/1.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.36/1.46 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 2.36/1.46 => ( in @ Xx @ A ) ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(setminusER_type,type,
% 2.36/1.46 setminusER: $o ).
% 2.36/1.46
% 2.36/1.46 thf(setminusER,definition,
% 2.36/1.46 ( setminusER
% 2.36/1.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.36/1.46 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 2.36/1.46 => ~ ( in @ Xx @ B ) ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(setminusSubset2_type,type,
% 2.36/1.46 setminusSubset2: $o ).
% 2.36/1.46
% 2.36/1.46 thf(setminusSubset2,definition,
% 2.36/1.46 ( setminusSubset2
% 2.36/1.46 = ( ! [A: $i,B: $i] :
% 2.36/1.46 ( ( subset @ A @ B )
% 2.36/1.46 => ( ( setminus @ A @ B )
% 2.36/1.46 = emptyset ) ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(setminusERneg_type,type,
% 2.36/1.46 setminusERneg: $o ).
% 2.36/1.46
% 2.36/1.46 thf(setminusERneg,definition,
% 2.36/1.46 ( setminusERneg
% 2.36/1.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.36/1.46 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 2.36/1.46 => ( ( in @ Xx @ A )
% 2.36/1.46 => ( in @ Xx @ B ) ) ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(setminusELneg_type,type,
% 2.36/1.46 setminusELneg: $o ).
% 2.36/1.46
% 2.36/1.46 thf(setminusELneg,definition,
% 2.36/1.46 ( setminusELneg
% 2.36/1.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.36/1.46 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 2.36/1.46 => ( ~ ( in @ Xx @ B )
% 2.36/1.46 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(setminusILneg_type,type,
% 2.36/1.46 setminusILneg: $o ).
% 2.36/1.46
% 2.36/1.46 thf(setminusILneg,definition,
% 2.36/1.46 ( setminusILneg
% 2.36/1.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.36/1.46 ( ~ ( in @ Xx @ A )
% 2.36/1.46 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(setminusIRneg_type,type,
% 2.36/1.46 setminusIRneg: $o ).
% 2.36/1.46
% 2.36/1.46 thf(setminusIRneg,definition,
% 2.36/1.46 ( setminusIRneg
% 2.36/1.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.36/1.46 ( ( in @ Xx @ B )
% 2.36/1.46 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(setminusLsub_type,type,
% 2.36/1.46 setminusLsub: $o ).
% 2.36/1.46
% 2.36/1.46 thf(setminusLsub,definition,
% 2.36/1.46 ( setminusLsub
% 2.36/1.46 = ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(setminusSubset1_type,type,
% 2.36/1.46 setminusSubset1: $o ).
% 2.36/1.46
% 2.36/1.46 thf(setminusSubset1,definition,
% 2.36/1.46 ( setminusSubset1
% 2.36/1.46 = ( ! [A: $i,B: $i] :
% 2.36/1.46 ( ( ( setminus @ A @ B )
% 2.36/1.46 = emptyset )
% 2.36/1.46 => ( subset @ A @ B ) ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(symdiff_type,type,
% 2.36/1.46 symdiff: $i > $i > $i ).
% 2.36/1.46
% 2.36/1.46 thf(symdiffE_type,type,
% 2.36/1.46 symdiffE: $o ).
% 2.36/1.46
% 2.36/1.46 thf(symdiffE,definition,
% 2.36/1.46 ( symdiffE
% 2.36/1.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.36/1.46 ( ( in @ Xx @ ( symdiff @ A @ B ) )
% 2.36/1.46 => ! [Xphi: $o] :
% 2.36/1.46 ( ( ( in @ Xx @ A )
% 2.36/1.46 => ( ~ ( in @ Xx @ B )
% 2.36/1.46 => Xphi ) )
% 2.36/1.46 => ( ( ~ ( in @ Xx @ A )
% 2.36/1.46 => ( ( in @ Xx @ B )
% 2.36/1.46 => Xphi ) )
% 2.36/1.46 => Xphi ) ) ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(symdiffI1_type,type,
% 2.36/1.46 symdiffI1: $o ).
% 2.36/1.46
% 2.36/1.46 thf(symdiffI1,definition,
% 2.36/1.46 ( symdiffI1
% 2.36/1.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.36/1.46 ( ( in @ Xx @ A )
% 2.36/1.46 => ( ~ ( in @ Xx @ B )
% 2.36/1.46 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(symdiffI2_type,type,
% 2.36/1.46 symdiffI2: $o ).
% 2.36/1.46
% 2.36/1.46 thf(symdiffI2,definition,
% 2.36/1.46 ( symdiffI2
% 2.36/1.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.36/1.46 ( ~ ( in @ Xx @ A )
% 2.36/1.46 => ( ( in @ Xx @ B )
% 2.36/1.46 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(symdiffIneg1_type,type,
% 2.36/1.46 symdiffIneg1: $o ).
% 2.36/1.46
% 2.36/1.46 thf(symdiffIneg1,definition,
% 2.36/1.46 ( symdiffIneg1
% 2.36/1.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.36/1.46 ( ( in @ Xx @ A )
% 2.36/1.46 => ( ( in @ Xx @ B )
% 2.36/1.46 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(symdiffIneg2_type,type,
% 2.36/1.46 symdiffIneg2: $o ).
% 2.36/1.46
% 2.36/1.46 thf(symdiffIneg2,definition,
% 2.36/1.46 ( symdiffIneg2
% 2.36/1.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.36/1.46 ( ~ ( in @ Xx @ A )
% 2.36/1.46 => ( ~ ( in @ Xx @ B )
% 2.36/1.46 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(iskpair_type,type,
% 2.36/1.46 iskpair: $i > $o ).
% 2.36/1.46
% 2.36/1.46 thf(iskpair,definition,
% 2.36/1.46 ( iskpair
% 2.36/1.46 = ( ^ [A: $i] :
% 2.36/1.46 ? [Xx: $i] :
% 2.36/1.46 ( ( in @ Xx @ ( setunion @ A ) )
% 2.36/1.46 & ? [Xy: $i] :
% 2.36/1.46 ( ( in @ Xy @ ( setunion @ A ) )
% 2.36/1.46 & ( A
% 2.36/1.46 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(secondinupair_type,type,
% 2.36/1.46 secondinupair: $o ).
% 2.36/1.46
% 2.36/1.46 thf(secondinupair,definition,
% 2.36/1.46 ( secondinupair
% 2.36/1.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(setukpairIL_type,type,
% 2.36/1.46 setukpairIL: $o ).
% 2.36/1.46
% 2.36/1.46 thf(setukpairIL,definition,
% 2.36/1.46 ( setukpairIL
% 2.36/1.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(setukpairIR_type,type,
% 2.36/1.46 setukpairIR: $o ).
% 2.36/1.46
% 2.36/1.46 thf(setukpairIR,definition,
% 2.36/1.46 ( setukpairIR
% 2.36/1.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(kpairiskpair_type,type,
% 2.36/1.46 kpairiskpair: $o ).
% 2.36/1.46
% 2.36/1.46 thf(kpairiskpair,definition,
% 2.36/1.46 ( kpairiskpair
% 2.36/1.46 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(kpair_type,type,
% 2.36/1.46 kpair: $i > $i > $i ).
% 2.36/1.46
% 2.36/1.46 thf(kpair,definition,
% 2.36/1.46 ( kpair
% 2.36/1.46 = ( ^ [Xx: $i,Xy: $i] : ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(kpairp_type,type,
% 2.36/1.46 kpairp: $o ).
% 2.36/1.46
% 2.36/1.46 thf(kpairp,definition,
% 2.36/1.46 ( kpairp
% 2.36/1.46 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(cartprod_type,type,
% 2.36/1.46 cartprod: $i > $i > $i ).
% 2.36/1.46
% 2.36/1.46 thf(cartprod,definition,
% 2.36/1.46 ( cartprod
% 2.36/1.46 = ( ^ [A: $i,B: $i] :
% 2.36/1.46 ( dsetconstr @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) )
% 2.36/1.46 @ ^ [Xx: $i] :
% 2.36/1.46 ? [Xy: $i] :
% 2.36/1.46 ( ( in @ Xy @ A )
% 2.36/1.46 & ? [Xz: $i] :
% 2.36/1.46 ( ( in @ Xz @ B )
% 2.36/1.46 & ( Xx
% 2.36/1.46 = ( kpair @ Xy @ Xz ) ) ) ) ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(singletonsubset_type,type,
% 2.36/1.46 singletonsubset: $o ).
% 2.36/1.46
% 2.36/1.46 thf(singletonsubset,definition,
% 2.36/1.46 ( singletonsubset
% 2.36/1.46 = ( ! [A: $i,Xx: $i] :
% 2.36/1.46 ( ( in @ Xx @ A )
% 2.36/1.46 => ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(singletoninpowerset_type,type,
% 2.36/1.46 singletoninpowerset: $o ).
% 2.36/1.46
% 2.36/1.46 thf(singletoninpowerset,definition,
% 2.36/1.46 ( singletoninpowerset
% 2.36/1.46 = ( ! [A: $i,Xx: $i] :
% 2.36/1.46 ( ( in @ Xx @ A )
% 2.36/1.46 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(singletoninpowunion_type,type,
% 2.36/1.46 singletoninpowunion: $o ).
% 2.36/1.46
% 2.36/1.46 thf(singletoninpowunion,definition,
% 2.36/1.46 ( singletoninpowunion
% 2.36/1.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.36/1.46 ( ( in @ Xx @ A )
% 2.36/1.46 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(upairset2E_type,type,
% 2.36/1.46 upairset2E: $o ).
% 2.36/1.46
% 2.36/1.46 thf(upairset2E,definition,
% 2.36/1.46 ( upairset2E
% 2.36/1.46 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.36/1.46 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 2.36/1.46 => ( ( Xz = Xx )
% 2.36/1.46 | ( Xz = Xy ) ) ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(upairsubunion_type,type,
% 2.36/1.46 upairsubunion: $o ).
% 2.36/1.46
% 2.36/1.46 thf(upairsubunion,definition,
% 2.36/1.46 ( upairsubunion
% 2.36/1.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.36/1.46 ( ( in @ Xx @ A )
% 2.36/1.46 => ! [Xy: $i] :
% 2.36/1.46 ( ( in @ Xy @ B )
% 2.36/1.46 => ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(upairinpowunion_type,type,
% 2.36/1.46 upairinpowunion: $o ).
% 2.36/1.46
% 2.36/1.46 thf(upairinpowunion,definition,
% 2.36/1.46 ( upairinpowunion
% 2.36/1.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.36/1.46 ( ( in @ Xx @ A )
% 2.36/1.46 => ! [Xy: $i] :
% 2.36/1.46 ( ( in @ Xy @ B )
% 2.36/1.46 => ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 2.36/1.46
% 2.36/1.46 thf(ubforcartprodlem1,conjecture,
% 2.36/1.46 ( setextAx
% 2.36/1.46 => ( emptysetAx
% 2.36/1.46 => ( setadjoinAx
% 2.36/1.46 => ( powersetAx
% 2.36/1.46 => ( setunionAx
% 2.36/1.46 => ( omega0Ax
% 2.36/1.46 => ( omegaSAx
% 2.36/1.46 => ( omegaIndAx
% 2.36/1.46 => ( replAx
% 2.36/1.46 => ( foundationAx
% 2.36/1.46 => ( wellorderingAx
% 2.36/1.46 => ( descrp
% 2.36/1.46 => ( dsetconstrI
% 2.36/1.46 => ( dsetconstrEL
% 2.36/1.46 => ( dsetconstrER
% 2.36/1.46 => ( exuE1
% 2.36/1.46 => ( prop2setE
% 2.36/1.46 => ( emptysetE
% 2.36/1.46 => ( emptysetimpfalse
% 2.36/1.46 => ( notinemptyset
% 2.36/1.46 => ( exuE3e
% 2.36/1.46 => ( setext
% 2.36/1.46 => ( emptyI
% 2.36/1.46 => ( noeltsimpempty
% 2.36/1.46 => ( setbeta
% 2.36/1.46 => ( nonemptyE1
% 2.36/1.46 => ( nonemptyI
% 2.36/1.46 => ( nonemptyI1
% 2.36/1.46 => ( setadjoinIL
% 2.36/1.46 => ( emptyinunitempty
% 2.36/1.46 => ( setadjoinIR
% 2.36/1.46 => ( setadjoinE
% 2.36/1.46 => ( setadjoinOr
% 2.36/1.46 => ( setoftrueEq
% 2.36/1.46 => ( powersetI
% 2.36/1.46 => ( emptyinPowerset
% 2.36/1.46 => ( emptyInPowerset
% 2.36/1.46 => ( powersetE
% 2.36/1.46 => ( setunionI
% 2.36/1.46 => ( setunionE
% 2.36/1.46 => ( subPowSU
% 2.36/1.46 => ( exuE2
% 2.36/1.46 => ( nonemptyImpWitness
% 2.36/1.46 => ( uniqinunit
% 2.36/1.46 => ( notinsingleton
% 2.36/1.46 => ( eqinunit
% 2.36/1.46 => ( singletonsswitch
% 2.36/1.46 => ( upairsetE
% 2.36/1.46 => ( upairsetIL
% 2.36/1.46 => ( upairsetIR
% 2.36/1.46 => ( emptyE1
% 2.36/1.46 => ( vacuousDall
% 2.36/1.46 => ( quantDeMorgan1
% 2.36/1.46 => ( quantDeMorgan2
% 2.36/1.46 => ( quantDeMorgan3
% 2.36/1.46 => ( quantDeMorgan4
% 2.36/1.46 => ( prop2setI
% 2.36/1.46 => ( prop2set2propI
% 2.36/1.46 => ( notdexE
% 2.36/1.46 => ( notdallE
% 2.36/1.46 => ( exuI1
% 2.36/1.46 => ( exuI3
% 2.36/1.46 => ( exuI2
% 2.36/1.46 => ( inCongP
% 2.36/1.46 => ( in__Cong
% 2.36/1.46 => ( exuE3u
% 2.36/1.46 => ( exu__Cong
% 2.36/1.46 => ( emptyset__Cong
% 2.36/1.46 => ( setadjoin__Cong
% 2.36/1.46 => ( powerset__Cong
% 2.36/1.46 => ( setunion__Cong
% 2.36/1.46 => ( omega__Cong
% 2.36/1.46 => ( exuEu
% 2.36/1.46 => ( descr__Cong
% 2.36/1.46 => ( dsetconstr__Cong
% 2.36/1.46 => ( subsetI1
% 2.36/1.46 => ( eqimpsubset2
% 2.36/1.46 => ( eqimpsubset1
% 2.36/1.46 => ( subsetI2
% 2.36/1.46 => ( emptysetsubset
% 2.36/1.46 => ( subsetE
% 2.36/1.46 => ( subsetE2
% 2.36/1.46 => ( notsubsetI
% 2.36/1.46 => ( notequalI1
% 2.36/1.46 => ( notequalI2
% 2.36/1.46 => ( subsetRefl
% 2.36/1.46 => ( subsetTrans
% 2.36/1.46 => ( setadjoinSub
% 2.36/1.46 => ( setadjoinSub2
% 2.36/1.46 => ( subset2powerset
% 2.36/1.46 => ( setextsub
% 2.36/1.46 => ( subsetemptysetimpeq
% 2.36/1.46 => ( powersetI1
% 2.36/1.46 => ( powersetE1
% 2.36/1.46 => ( inPowerset
% 2.36/1.46 => ( powersetsubset
% 2.36/1.46 => ( sepInPowerset
% 2.36/1.46 => ( sepSubset
% 2.36/1.46 => ( binunionIL
% 2.36/1.46 => ( upairset2IR
% 2.36/1.46 => ( binunionIR
% 2.36/1.46 => ( binunionEcases
% 2.36/1.46 => ( binunionE
% 2.36/1.46 => ( binunionLsub
% 2.36/1.46 => ( binunionRsub
% 2.36/1.46 => ( binintersectI
% 2.36/1.46 => ( binintersectSubset5
% 2.36/1.46 => ( binintersectEL
% 2.36/1.46 => ( binintersectLsub
% 2.36/1.46 => ( binintersectSubset2
% 2.36/1.46 => ( binintersectSubset3
% 2.36/1.46 => ( binintersectER
% 2.36/1.46 => ( disjointsetsI1
% 2.36/1.46 => ( binintersectRsub
% 2.36/1.46 => ( binintersectSubset4
% 2.36/1.46 => ( binintersectSubset1
% 2.36/1.46 => ( bs114d
% 2.36/1.46 => ( setminusI
% 2.36/1.46 => ( setminusEL
% 2.36/1.46 => ( setminusER
% 2.36/1.46 => ( setminusSubset2
% 2.36/1.46 => ( setminusERneg
% 2.36/1.46 => ( setminusELneg
% 2.36/1.46 => ( setminusILneg
% 2.36/1.46 => ( setminusIRneg
% 2.36/1.46 => ( setminusLsub
% 2.36/1.46 => ( setminusSubset1
% 2.36/1.46 => ( symdiffE
% 2.36/1.46 => ( symdiffI1
% 2.36/1.46 => ( symdiffI2
% 2.36/1.46 => ( symdiffIneg1
% 2.36/1.46 => ( symdiffIneg2
% 2.36/1.46 => ( secondinupair
% 2.36/1.46 => ( setukpairIL
% 2.36/1.46 => ( setukpairIR
% 2.36/1.46 => ( kpairiskpair
% 2.36/1.46 => ( kpairp
% 2.36/1.46 => ( singletonsubset
% 2.36/1.46 => ( singletoninpowerset
% 2.36/1.46 => ( singletoninpowunion
% 2.36/1.46 => ( upairset2E
% 2.36/1.46 => ( upairsubunion
% 2.36/1.46 => ( upairinpowunion
% 2.36/1.46 => ! [A: $i,B: $i,Xx: $i] :
% 2.36/1.46 ( ( in @ Xx @ A )
% 2.36/1.46 => ! [Xy: $i] :
% 2.36/1.46 ( ( in @ Xy @ B )
% 2.36/1.46 => ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.36/1.46 ------------------------
% 2.36/1.47 % (12583)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_12319 for (2999ds/4Mi)
% 2.36/1.47 % (12584)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_12319 for (2999ds/27Mi)
% 2.36/1.47 % (12583)Instruction limit reached!
% 2.36/1.47 % (12583)------------------------------
% 2.36/1.47 % (12583)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.36/1.47 % (12583)Termination reason: Unknown
% 2.36/1.47 % (12583)Termination phase: shuffling
% 2.36/1.47
% 2.36/1.47 % (12583)Memory used [KB]: 1279
% 2.36/1.47 % (12583)Time elapsed: 0.003 s
% 2.36/1.47 % (12583)Instructions burned: 5 (million)
% 2.36/1.47 % (12583)------------------------------
% 2.36/1.47 % (12583)------------------------------
% 2.36/1.48 % (12582)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_12319 for (2999ds/183Mi)
% 2.36/1.48 % (12585)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_12319 for (2999ds/2Mi)
% 2.36/1.48 % (12586)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_12319 for (2999ds/2Mi)
% 2.36/1.48 % (12587)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_12319 for (2999ds/275Mi)
% 2.36/1.48 % (12588)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_12319 for (2999ds/18Mi)
% 2.36/1.48 % (12584)Instruction limit reached!
% 2.36/1.48 % (12584)------------------------------
% 2.36/1.48 % (12584)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.36/1.48 % (12584)Termination reason: Unknown
% 2.36/1.48 % (12584)Termination phase: Property scanning
% 2.36/1.48
% 2.36/1.48 % (12584)Memory used [KB]: 1663
% 2.36/1.48 % (12584)Time elapsed: 0.009 s
% 2.36/1.48 % (12584)Instructions burned: 27 (million)
% 2.36/1.48 % (12584)------------------------------
% 2.36/1.48 % (12584)------------------------------
% 2.36/1.48 % (12585)Instruction limit reached!
% 2.36/1.48 % (12585)------------------------------
% 2.36/1.48 % (12585)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.36/1.48 % (12585)Termination reason: Unknown
% 2.36/1.48 % (12585)Termination phase: shuffling
% 2.36/1.48
% 2.36/1.48 % (12585)Memory used [KB]: 1279
% 2.36/1.48 % (12585)Time elapsed: 0.004 s
% 2.36/1.48 % (12585)Instructions burned: 3 (million)
% 2.36/1.48 % (12585)------------------------------
% 2.36/1.48 % (12585)------------------------------
% 2.36/1.48 % (12586)Instruction limit reached!
% 2.36/1.48 % (12586)------------------------------
% 2.36/1.48 % (12586)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.36/1.48 % (12586)Termination reason: Unknown
% 2.36/1.48 % (12586)Termination phase: shuffling
% 2.36/1.48
% 2.36/1.48 % (12586)Memory used [KB]: 1279
% 2.36/1.48 % (12586)Time elapsed: 0.004 s
% 2.36/1.48 % (12586)Instructions burned: 4 (million)
% 2.36/1.48 % (12586)------------------------------
% 2.36/1.48 % (12586)------------------------------
% 2.36/1.48 % (12589)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_12319 for (2999ds/3Mi)
% 2.36/1.48 % (12589)Instruction limit reached!
% 2.36/1.48 % (12589)------------------------------
% 2.36/1.48 % (12589)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.36/1.48 % (12589)Termination reason: Unknown
% 2.36/1.48 % (12589)Termination phase: shuffling
% 2.36/1.48
% 2.36/1.48 % (12589)Memory used [KB]: 1279
% 2.36/1.48 % (12589)Time elapsed: 0.002 s
% 2.36/1.48 % (12589)Instructions burned: 4 (million)
% 2.36/1.48 % (12589)------------------------------
% 2.36/1.48 % (12589)------------------------------
% 2.36/1.49 % (12590)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_12319 for (2999ds/37Mi)
% 2.36/1.49 % (12588)Instruction limit reached!
% 2.36/1.49 % (12588)------------------------------
% 2.36/1.49 % (12588)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.36/1.49 % (12588)Termination reason: Unknown
% 2.36/1.49 % (12588)Termination phase: Preprocessing 1
% 2.36/1.49
% 2.36/1.49 % (12588)Memory used [KB]: 1535
% 2.36/1.49 % (12588)Time elapsed: 0.013 s
% 2.36/1.49 % (12588)Instructions burned: 19 (million)
% 2.36/1.49 % (12588)------------------------------
% 2.36/1.49 % (12588)------------------------------
% 2.36/1.49 % (12593)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_12319 for (2999ds/1041Mi)
% 2.46/1.50 % (12591)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_12319 for (2999ds/15Mi)
% 2.46/1.50 % (12592)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_12319 for (2999ds/3Mi)
% 2.46/1.50 % (12590)Instruction limit reached!
% 2.46/1.50 % (12590)------------------------------
% 2.46/1.50 % (12590)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.46/1.50 % (12590)Termination reason: Unknown
% 2.46/1.50 % (12590)Termination phase: Clausification
% 2.46/1.50
% 2.46/1.50 % (12590)Memory used [KB]: 1663
% 2.46/1.50 % (12590)Time elapsed: 0.012 s
% 2.46/1.50 % (12590)Instructions burned: 37 (million)
% 2.46/1.50 % (12590)------------------------------
% 2.46/1.50 % (12590)------------------------------
% 2.46/1.50 % (12592)Instruction limit reached!
% 2.46/1.50 % (12592)------------------------------
% 2.46/1.50 % (12592)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.46/1.50 % (12592)Termination reason: Unknown
% 2.46/1.50 % (12592)Termination phase: shuffling
% 2.46/1.50
% 2.46/1.50 % (12592)Memory used [KB]: 1279
% 2.46/1.50 % (12592)Time elapsed: 0.004 s
% 2.46/1.50 % (12592)Instructions burned: 4 (million)
% 2.46/1.50 % (12592)------------------------------
% 2.46/1.50 % (12592)------------------------------
% 2.46/1.51 % (12591)Instruction limit reached!
% 2.46/1.51 % (12591)------------------------------
% 2.46/1.51 % (12591)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.46/1.51 % (12591)Termination reason: Unknown
% 2.46/1.51 % (12591)Termination phase: Property scanning
% 2.46/1.51
% 2.46/1.51 % (12591)Memory used [KB]: 1535
% 2.46/1.51 % (12591)Time elapsed: 0.009 s
% 2.46/1.51 % (12591)Instructions burned: 16 (million)
% 2.46/1.51 % (12591)------------------------------
% 2.46/1.51 % (12591)------------------------------
% 2.46/1.51 % (12594)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_12319 for (2999ds/7Mi)
% 2.46/1.51 % (12595)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_12319 for (2999ds/16Mi)
% 2.46/1.51 % (12594)Instruction limit reached!
% 2.46/1.51 % (12594)------------------------------
% 2.46/1.51 % (12594)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.46/1.51 % (12594)Termination reason: Unknown
% 2.46/1.51 % (12594)Termination phase: shuffling
% 2.46/1.51
% 2.46/1.51 % (12594)Memory used [KB]: 1279
% 2.46/1.51 % (12594)Time elapsed: 0.005 s
% 2.46/1.51 % (12594)Instructions burned: 7 (million)
% 2.46/1.51 % (12594)------------------------------
% 2.46/1.51 % (12594)------------------------------
% 2.46/1.52 % (12595)Instruction limit reached!
% 2.46/1.52 % (12595)------------------------------
% 2.46/1.52 % (12595)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.46/1.52 % (12595)Termination reason: Unknown
% 2.46/1.52 % (12595)Termination phase: shuffling
% 2.46/1.52
% 2.46/1.52 % (12595)Memory used [KB]: 1663
% 2.46/1.52 % (12595)Time elapsed: 0.007 s
% 2.46/1.52 % (12595)Instructions burned: 18 (million)
% 2.46/1.52 % (12595)------------------------------
% 2.46/1.52 % (12595)------------------------------
% 2.46/1.52 % (12597)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_12319 for (2999ds/3Mi)
% 2.46/1.52 % (12596)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_12319 for (2999ds/3Mi)
% 2.46/1.52 % (12597)Instruction limit reached!
% 2.46/1.52 % (12597)------------------------------
% 2.46/1.52 % (12597)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.46/1.52 % (12597)Termination reason: Unknown
% 2.46/1.52 % (12597)Termination phase: shuffling
% 2.46/1.52
% 2.46/1.52 % (12597)Memory used [KB]: 1279
% 2.46/1.52 % (12597)Time elapsed: 0.003 s
% 2.46/1.52 % (12597)Instructions burned: 5 (million)
% 2.46/1.52 % (12597)------------------------------
% 2.46/1.52 % (12597)------------------------------
% 2.46/1.52 % (12596)Instruction limit reached!
% 2.46/1.52 % (12596)------------------------------
% 2.46/1.52 % (12596)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.46/1.52 % (12596)Termination reason: Unknown
% 2.46/1.52 % (12596)Termination phase: shuffling
% 2.46/1.52
% 2.46/1.52 % (12596)Memory used [KB]: 1279
% 2.46/1.52 % (12596)Time elapsed: 0.004 s
% 2.46/1.52 % (12596)Instructions burned: 4 (million)
% 2.46/1.52 % (12596)------------------------------
% 2.46/1.52 % (12596)------------------------------
% 2.46/1.53 % (12599)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_12319 for (2999ds/3Mi)
% 2.46/1.53 % (12599)Instruction limit reached!
% 2.46/1.53 % (12599)------------------------------
% 2.46/1.53 % (12599)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.46/1.53 % (12599)Termination reason: Unknown
% 2.46/1.53 % (12599)Termination phase: shuffling
% 2.46/1.53
% 2.46/1.53 % (12599)Memory used [KB]: 1279
% 2.46/1.53 % (12599)Time elapsed: 0.003 s
% 2.46/1.53 % (12599)Instructions burned: 4 (million)
% 2.46/1.53 % (12599)------------------------------
% 2.46/1.53 % (12599)------------------------------
% 2.46/1.53 % (12600)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_12319 for (2999ds/4Mi)
% 2.46/1.53 % (12598)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_12319 for (2999ds/7Mi)
% 2.46/1.53 % (12600)Instruction limit reached!
% 2.46/1.53 % (12600)------------------------------
% 2.46/1.53 % (12600)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.46/1.53 % (12600)Termination reason: Unknown
% 2.46/1.53 % (12600)Termination phase: shuffling
% 2.46/1.53
% 2.46/1.53 % (12600)Memory used [KB]: 1279
% 2.46/1.53 % (12600)Time elapsed: 0.003 s
% 2.46/1.53 % (12600)Instructions burned: 4 (million)
% 2.46/1.53 % (12600)------------------------------
% 2.46/1.53 % (12600)------------------------------
% 2.46/1.53 % (12598)Instruction limit reached!
% 2.46/1.53 % (12598)------------------------------
% 2.46/1.53 % (12598)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.46/1.53 % (12598)Termination reason: Unknown
% 2.46/1.53 % (12598)Termination phase: shuffling
% 2.46/1.53
% 2.46/1.53 % (12598)Memory used [KB]: 1407
% 2.46/1.53 % (12598)Time elapsed: 0.006 s
% 2.46/1.53 % (12598)Instructions burned: 8 (million)
% 2.46/1.53 % (12598)------------------------------
% 2.46/1.53 % (12598)------------------------------
% 2.46/1.54 % (12601)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_12319 for (2999ds/18Mi)
% 2.46/1.54 % (12602)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_12319 for (2999ds/710Mi)
% 2.46/1.54 % (12603)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_12319 for (2999ds/6Mi)
% 2.46/1.54 % (12603)Instruction limit reached!
% 2.46/1.54 % (12603)------------------------------
% 2.46/1.54 % (12603)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.46/1.54 % (12603)Termination reason: Unknown
% 2.46/1.54 % (12603)Termination phase: shuffling
% 2.46/1.54
% 2.46/1.54 % (12603)Memory used [KB]: 1407
% 2.46/1.54 % (12603)Time elapsed: 0.004 s
% 2.46/1.54 % (12603)Instructions burned: 8 (million)
% 2.46/1.54 % (12603)------------------------------
% 2.46/1.54 % (12603)------------------------------
% 2.46/1.55 % (12601)Instruction limit reached!
% 2.46/1.55 % (12601)------------------------------
% 2.46/1.55 % (12601)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.46/1.55 % (12601)Termination reason: Unknown
% 2.46/1.55 % (12601)Termination phase: shuffling
% 2.46/1.55
% 2.46/1.55 % (12601)Memory used [KB]: 1535
% 2.46/1.55 % (12601)Time elapsed: 0.009 s
% 2.46/1.55 % (12601)Instructions burned: 18 (million)
% 2.46/1.55 % (12601)------------------------------
% 2.46/1.55 % (12601)------------------------------
% 2.46/1.55 % (12604)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_12319 for (2999ds/902Mi)
% 2.46/1.55 % (12605)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_12319 for (2999ds/21Mi)
% 2.46/1.56 % (12606)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_12319 for (2999ds/5Mi)
% 2.46/1.56 % (12606)Instruction limit reached!
% 2.46/1.56 % (12606)------------------------------
% 2.46/1.56 % (12606)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.46/1.56 % (12606)Termination reason: Unknown
% 2.46/1.56 % (12606)Termination phase: shuffling
% 2.46/1.56
% 2.46/1.56 % (12606)Memory used [KB]: 1279
% 2.46/1.56 % (12606)Time elapsed: 0.003 s
% 2.46/1.56 % (12606)Instructions burned: 5 (million)
% 2.46/1.56 % (12606)------------------------------
% 2.46/1.56 % (12606)------------------------------
% 2.46/1.56 % (12605)Instruction limit reached!
% 2.46/1.56 % (12605)------------------------------
% 2.46/1.56 % (12605)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.46/1.56 % (12605)Termination reason: Unknown
% 2.46/1.56 % (12605)Termination phase: shuffling
% 2.46/1.56
% 2.46/1.56 % (12605)Memory used [KB]: 1663
% 2.46/1.56 % (12605)Time elapsed: 0.008 s
% 2.46/1.56 % (12605)Instructions burned: 21 (million)
% 2.46/1.56 % (12605)------------------------------
% 2.46/1.56 % (12605)------------------------------
% 2.46/1.57 % (12607)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_12319 for (2999ds/6Mi)
% 2.46/1.57 % (12608)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_12319 for (2999ds/377Mi)
% 2.46/1.57 % (12607)Instruction limit reached!
% 2.46/1.57 % (12607)------------------------------
% 2.46/1.57 % (12607)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.46/1.57 % (12607)Termination reason: Unknown
% 2.46/1.57 % (12607)Termination phase: shuffling
% 2.46/1.57
% 2.46/1.57 % (12607)Memory used [KB]: 1407
% 2.46/1.57 % (12607)Time elapsed: 0.004 s
% 2.46/1.57 % (12607)Instructions burned: 7 (million)
% 2.46/1.57 % (12607)------------------------------
% 2.46/1.57 % (12607)------------------------------
% 2.46/1.57 % (12582)Instruction limit reached!
% 2.46/1.57 % (12582)------------------------------
% 2.46/1.57 % (12582)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.46/1.57 % (12582)Termination reason: Unknown
% 2.46/1.57 % (12582)Termination phase: Saturation
% 2.46/1.57
% 2.46/1.57 % (12582)Memory used [KB]: 7164
% 2.46/1.57 % (12582)Time elapsed: 0.095 s
% 2.46/1.57 % (12582)Instructions burned: 184 (million)
% 2.46/1.57 % (12582)------------------------------
% 2.46/1.57 % (12582)------------------------------
% 2.46/1.58 % (12609)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_12319 for (2998ds/779Mi)
% 2.46/1.58 % (12611)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_12319 for (2998ds/19Mi)
% 2.46/1.59 % (12611)Instruction limit reached!
% 2.46/1.59 % (12611)------------------------------
% 2.46/1.59 % (12611)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.46/1.59 % (12611)Termination reason: Unknown
% 2.46/1.59 % (12611)Termination phase: shuffling
% 2.46/1.59
% 2.46/1.59 % (12611)Memory used [KB]: 1663
% 2.46/1.59 % (12611)Time elapsed: 0.007 s
% 2.46/1.59 % (12611)Instructions burned: 21 (million)
% 2.46/1.59 % (12611)------------------------------
% 2.46/1.59 % (12611)------------------------------
% 2.46/1.60 % (12612)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_12319 for (2998ds/879Mi)
% 2.46/1.62 % (12587)Instruction limit reached!
% 2.46/1.62 % (12587)------------------------------
% 2.46/1.62 % (12587)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.46/1.62 % (12587)Termination reason: Unknown
% 2.46/1.62 % (12587)Termination phase: Saturation
% 2.46/1.62
% 2.46/1.62 % (12587)Memory used [KB]: 7931
% 2.46/1.62 % (12587)Time elapsed: 0.141 s
% 2.46/1.62 % (12587)Instructions burned: 277 (million)
% 2.46/1.62 % (12587)------------------------------
% 2.46/1.62 % (12587)------------------------------
% 2.46/1.63 % (12613)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_12319 for (2998ds/17Mi)
% 2.46/1.63 % (12613)Instruction limit reached!
% 2.46/1.63 % (12613)------------------------------
% 2.46/1.63 % (12613)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.46/1.63 % (12613)Termination reason: Unknown
% 2.46/1.63 % (12613)Termination phase: shuffling
% 2.46/1.63
% 2.46/1.63 % (12613)Memory used [KB]: 1663
% 2.46/1.63 % (12613)Time elapsed: 0.006 s
% 2.46/1.63 % (12613)Instructions burned: 17 (million)
% 2.46/1.63 % (12613)------------------------------
% 2.46/1.63 % (12613)------------------------------
% 2.46/1.65 % (12614)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_12319 for (2998ds/3Mi)
% 2.46/1.65 % (12614)Instruction limit reached!
% 2.46/1.65 % (12614)------------------------------
% 2.46/1.65 % (12614)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.46/1.65 % (12614)Termination reason: Unknown
% 2.46/1.65 % (12614)Termination phase: shuffling
% 2.46/1.65
% 2.46/1.65 % (12614)Memory used [KB]: 1279
% 2.46/1.65 % (12614)Time elapsed: 0.003 s
% 2.46/1.65 % (12614)Instructions burned: 4 (million)
% 2.46/1.65 % (12614)------------------------------
% 2.46/1.65 % (12614)------------------------------
% 2.46/1.66 % (12615)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_12319 for (2998ds/30Mi)
% 2.46/1.67 % (12615)Instruction limit reached!
% 2.46/1.67 % (12615)------------------------------
% 2.46/1.67 % (12615)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.46/1.67 % (12615)Termination reason: Unknown
% 2.46/1.67 % (12615)Termination phase: Property scanning
% 2.46/1.67
% 2.46/1.67 % (12615)Memory used [KB]: 1791
% 2.46/1.67 % (12615)Time elapsed: 0.011 s
% 2.46/1.67 % (12615)Instructions burned: 33 (million)
% 2.46/1.67 % (12615)------------------------------
% 2.46/1.67 % (12615)------------------------------
% 2.46/1.68 % (12616)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_12319 for (2998ds/127Mi)
% 2.46/1.69 % (12608)Instruction limit reached!
% 2.46/1.69 % (12608)------------------------------
% 2.46/1.69 % (12608)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.46/1.69 % (12608)Termination reason: Unknown
% 2.46/1.69 % (12608)Termination phase: Saturation
% 2.46/1.69
% 2.46/1.69 % (12608)Memory used [KB]: 7675
% 2.46/1.69 % (12608)Time elapsed: 0.123 s
% 2.46/1.69 % (12608)Instructions burned: 377 (million)
% 2.46/1.69 % (12608)------------------------------
% 2.46/1.69 % (12608)------------------------------
% 2.46/1.70 % (12617)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_12319 for (2997ds/100Mi)
% 2.46/1.71 % (12616)Instruction limit reached!
% 2.46/1.71 % (12616)------------------------------
% 2.46/1.71 % (12616)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.46/1.71 % (12616)Termination reason: Unknown
% 2.46/1.71 % (12616)Termination phase: Saturation
% 2.46/1.71
% 2.46/1.71 % (12616)Memory used [KB]: 6908
% 2.46/1.71 % (12616)Time elapsed: 0.038 s
% 2.46/1.71 % (12616)Instructions burned: 128 (million)
% 2.46/1.71 % (12616)------------------------------
% 2.46/1.71 % (12616)------------------------------
% 2.46/1.72 % (12618)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on DTF2THF_12319 for (2997ds/3Mi)
% 2.46/1.72 % (12618)Instruction limit reached!
% 2.46/1.72 % (12618)------------------------------
% 2.46/1.72 % (12618)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.46/1.72 % (12618)Termination reason: Unknown
% 2.46/1.72 % (12618)Termination phase: shuffling
% 2.46/1.72
% 2.46/1.72 % (12618)Memory used [KB]: 1279
% 2.46/1.72 % (12618)Time elapsed: 0.003 s
% 2.46/1.72 % (12618)Instructions burned: 5 (million)
% 2.46/1.72 % (12618)------------------------------
% 2.46/1.72 % (12618)------------------------------
% 2.46/1.73 % (12617)Instruction limit reached!
% 2.46/1.73 % (12617)------------------------------
% 2.46/1.73 % (12617)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.46/1.73 % (12617)Termination reason: Unknown
% 2.46/1.73 % (12617)Termination phase: Saturation
% 2.46/1.73
% 2.46/1.73 % (12617)Memory used [KB]: 6396
% 2.46/1.73 % (12617)Time elapsed: 0.031 s
% 2.46/1.73 % (12617)Instructions burned: 101 (million)
% 2.46/1.73 % (12617)------------------------------
% 2.46/1.73 % (12617)------------------------------
% 2.46/1.73 % (12619)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on DTF2THF_12319 for (2997ds/20Mi)
% 2.46/1.74 % (12619)Instruction limit reached!
% 2.46/1.74 % (12619)------------------------------
% 2.46/1.74 % (12619)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.46/1.74 % (12619)Termination reason: Unknown
% 2.46/1.74 % (12619)Termination phase: SInE selection
% 2.46/1.74
% 2.46/1.74 % (12619)Memory used [KB]: 1535
% 2.46/1.74 % (12619)Time elapsed: 0.008 s
% 2.46/1.74 % (12619)Instructions burned: 20 (million)
% 2.46/1.74 % (12619)------------------------------
% 2.46/1.74 % (12619)------------------------------
% 2.46/1.74 % (12620)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on DTF2THF_12319 for (2997ds/86Mi)
% 2.46/1.74 % (12593)Instruction limit reached!
% 2.46/1.74 % (12593)------------------------------
% 2.46/1.74 % (12593)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.46/1.74 % (12593)Termination reason: Unknown
% 2.46/1.74 % (12593)Termination phase: Saturation
% 2.46/1.74
% 2.46/1.74 % (12593)Memory used [KB]: 9083
% 2.46/1.74 % (12593)Time elapsed: 0.252 s
% 2.46/1.74 % (12593)Instructions burned: 1041 (million)
% 2.46/1.74 % (12593)------------------------------
% 2.46/1.74 % (12593)------------------------------
% 2.46/1.75 % (12621)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on DTF2THF_12319 for (2997ds/107Mi)
% 2.46/1.75 % (12622)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on DTF2THF_12319 for (2997ds/39Mi)
% 2.46/1.76 % (12602)Instruction limit reached!
% 2.46/1.76 % (12602)------------------------------
% 2.46/1.76 % (12602)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.46/1.76 % (12602)Termination reason: Unknown
% 2.46/1.76 % (12602)Termination phase: Saturation
% 2.46/1.76
% 2.46/1.76 % (12602)Memory used [KB]: 9083
% 2.46/1.76 % (12602)Time elapsed: 0.226 s
% 2.46/1.76 % (12602)Instructions burned: 711 (million)
% 2.46/1.76 % (12602)------------------------------
% 2.46/1.76 % (12602)------------------------------
% 2.46/1.76 % (12622)Instruction limit reached!
% 2.46/1.76 % (12622)------------------------------
% 2.46/1.76 % (12622)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.46/1.76 % (12622)Termination reason: Unknown
% 2.46/1.76 % (12622)Termination phase: Property scanning
% 2.46/1.76
% 2.46/1.76 % (12622)Memory used [KB]: 1663
% 2.46/1.76 % (12622)Time elapsed: 0.011 s
% 2.46/1.76 % (12622)Instructions burned: 39 (million)
% 2.46/1.76 % (12622)------------------------------
% 2.46/1.76 % (12622)------------------------------
% 2.46/1.77 % (12620)Instruction limit reached!
% 2.46/1.77 % (12620)------------------------------
% 2.46/1.77 % (12620)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.46/1.77 % (12620)Termination reason: Unknown
% 2.46/1.77 % (12620)Termination phase: Saturation
% 2.46/1.77
% 2.46/1.77 % (12620)Memory used [KB]: 6524
% 2.46/1.77 % (12620)Time elapsed: 0.026 s
% 2.46/1.77 % (12620)Instructions burned: 86 (million)
% 2.46/1.77 % (12620)------------------------------
% 2.46/1.77 % (12620)------------------------------
% 2.46/1.77 % (12623)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on DTF2THF_12319 for (2996ds/448Mi)
% 2.46/1.77 % (12624)lrs+10_1:512_au=on:fde=unused:lma=on:nm=32:plsq=on:plsqc=1:plsqr=16121663,131072:sfv=off:sp=const_max:ss=axioms:st=3.0:tgt=full:i=46:si=on:rtra=on_0 on DTF2THF_12319 for (2996ds/46Mi)
% 2.46/1.78 % (12625)lrs+10_1:10_au=on:av=off:cbe=off:cnfonf=lazy_pi_sigma_gen:ntd=on:plsq=on:plsqc=1:plsqr=32,1:i=98:si=on:rtra=on_0 on DTF2THF_12319 for (2996ds/98Mi)
% 2.46/1.78 % (12609)Instruction limit reached!
% 2.46/1.78 % (12609)------------------------------
% 2.46/1.78 % (12609)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.46/1.78 % (12609)Termination reason: Unknown
% 2.46/1.78 % (12609)Termination phase: Saturation
% 2.46/1.78
% 2.46/1.78 % (12609)Memory used [KB]: 6524
% 2.46/1.78 % (12609)Time elapsed: 0.197 s
% 2.46/1.78 % (12609)Instructions burned: 779 (million)
% 2.46/1.78 % (12609)------------------------------
% 2.46/1.78 % (12609)------------------------------
% 2.46/1.78 % (12621)Instruction limit reached!
% 2.46/1.78 % (12621)------------------------------
% 2.46/1.78 % (12621)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.46/1.78 % (12621)Termination reason: Unknown
% 2.46/1.78 % (12621)Termination phase: Saturation
% 2.46/1.78
% 2.46/1.78 % (12621)Memory used [KB]: 6780
% 2.46/1.78 % (12621)Time elapsed: 0.032 s
% 2.46/1.78 % (12621)Instructions burned: 108 (million)
% 2.46/1.78 % (12621)------------------------------
% 2.46/1.78 % (12621)------------------------------
% 2.46/1.79 % (12624)Instruction limit reached!
% 2.46/1.79 % (12624)------------------------------
% 2.46/1.79 % (12624)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.46/1.79 % (12624)Termination reason: Unknown
% 2.46/1.79 % (12624)Termination phase: Property scanning
% 2.46/1.79
% 2.46/1.79 % (12624)Memory used [KB]: 1791
% 2.46/1.79 % (12624)Time elapsed: 0.013 s
% 2.46/1.79 % (12624)Instructions burned: 47 (million)
% 2.46/1.79 % (12624)------------------------------
% 2.46/1.79 % (12624)------------------------------
% 2.46/1.79 % (12626)ott+1002_1:1_apa=on:au=on:bd=off:cnfonf=off:fd=off:sos=on:sp=weighted_frequency:i=507:si=on:rtra=on_0 on DTF2THF_12319 for (2996ds/507Mi)
% 2.46/1.79 % (12627)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=149:si=on:rtra=on_0 on DTF2THF_12319 for (2996ds/149Mi)
% 2.46/1.80 % (12628)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_12319 for (2996ds/39Mi)
% 2.46/1.80 % (12625)Instruction limit reached!
% 2.46/1.80 % (12625)------------------------------
% 2.46/1.80 % (12625)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.46/1.80 % (12625)Termination reason: Unknown
% 2.46/1.80 % (12625)Termination phase: Saturation
% 2.46/1.80
% 2.46/1.80 % (12625)Memory used [KB]: 1918
% 2.46/1.80 % (12625)Time elapsed: 0.029 s
% 2.46/1.80 % (12625)Instructions burned: 101 (million)
% 2.46/1.80 % (12625)------------------------------
% 2.46/1.80 % (12625)------------------------------
% 2.46/1.81 % (12628)Instruction limit reached!
% 2.46/1.81 % (12628)------------------------------
% 2.46/1.81 % (12628)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.46/1.81 % (12628)Termination reason: Unknown
% 2.46/1.81 % (12628)Termination phase: Property scanning
% 2.46/1.81
% 2.46/1.81 % (12628)Memory used [KB]: 1791
% 2.46/1.81 % (12628)Time elapsed: 0.012 s
% 2.46/1.81 % (12628)Instructions burned: 41 (million)
% 2.46/1.81 % (12628)------------------------------
% 2.46/1.81 % (12628)------------------------------
% 2.46/1.81 % (12629)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_12319 for (2996ds/6Mi)
% 2.46/1.81 % (12629)Instruction limit reached!
% 2.46/1.81 % (12629)------------------------------
% 2.46/1.81 % (12629)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.46/1.81 % (12629)Termination reason: Unknown
% 2.46/1.81 % (12629)Termination phase: shuffling
% 2.46/1.81
% 2.46/1.81 % (12629)Memory used [KB]: 1407
% 2.46/1.81 % (12629)Time elapsed: 0.004 s
% 2.46/1.81 % (12629)Instructions burned: 8 (million)
% 2.46/1.81 % (12629)------------------------------
% 2.46/1.81 % (12629)------------------------------
% 2.46/1.82 % (12630)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=1087:si=on:rtra=on_0 on DTF2THF_12319 for (2996ds/1087Mi)
% 2.46/1.83 % (12631)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_12319 for (2996ds/47Mi)
% 2.46/1.84 % (12627)Instruction limit reached!
% 2.46/1.84 % (12627)------------------------------
% 2.46/1.84 % (12627)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.46/1.84 % (12627)Termination reason: Unknown
% 2.46/1.84 % (12627)Termination phase: Saturation
% 2.46/1.84
% 2.46/1.84 % (12627)Memory used [KB]: 7164
% 2.46/1.84 % (12627)Time elapsed: 0.049 s
% 2.46/1.84 % (12627)Instructions burned: 150 (million)
% 2.46/1.84 % (12627)------------------------------
% 2.46/1.84 % (12627)------------------------------
% 2.46/1.84 % (12631)Instruction limit reached!
% 2.46/1.84 % (12631)------------------------------
% 2.46/1.84 % (12631)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.46/1.84 % (12631)Termination reason: Unknown
% 2.46/1.84 % (12631)Termination phase: Property scanning
% 2.46/1.84
% 2.46/1.84 % (12631)Memory used [KB]: 1791
% 2.46/1.84 % (12631)Time elapsed: 0.015 s
% 2.46/1.84 % (12631)Instructions burned: 47 (million)
% 2.46/1.84 % (12631)------------------------------
% 2.46/1.84 % (12631)------------------------------
% 2.46/1.84 % (12604)Instruction limit reached!
% 2.46/1.84 % (12604)------------------------------
% 2.46/1.84 % (12604)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.46/1.84 % (12604)Termination reason: Unknown
% 2.46/1.84 % (12604)Termination phase: Saturation
% 2.46/1.84
% 2.46/1.84 % (12604)Memory used [KB]: 9210
% 2.46/1.84 % (12604)Time elapsed: 0.293 s
% 2.46/1.84 % (12604)Instructions burned: 903 (million)
% 2.46/1.84 % (12604)------------------------------
% 2.46/1.84 % (12604)------------------------------
% 2.46/1.85 % (12632)lrs+1010_1:128_av=off:cbe=off:cnfonf=lazy_simp:fsr=off:ntd=on:ss=axioms:st=1.5:i=44:si=on:rtra=on_0 on DTF2THF_12319 for (2996ds/44Mi)
% 2.46/1.85 % (12633)dis+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=432:si=on:rtra=on_0 on DTF2THF_12319 for (2996ds/432Mi)
% 2.46/1.85 % (12634)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_12319 for (2996ds/62Mi)
% 2.46/1.86 % (12632)Instruction limit reached!
% 2.46/1.86 % (12632)------------------------------
% 2.46/1.86 % (12632)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.46/1.86 % (12632)Termination reason: Unknown
% 2.46/1.86 % (12632)Termination phase: Preprocessing 1
% 2.46/1.86
% 2.46/1.86 % (12632)Memory used [KB]: 1663
% 2.46/1.86 % (12632)Time elapsed: 0.014 s
% 2.46/1.86 % (12632)Instructions burned: 45 (million)
% 2.46/1.86 % (12632)------------------------------
% 2.46/1.86 % (12632)------------------------------
% 2.46/1.87 % (12635)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_12319 for (2996ds/31Mi)
% 2.46/1.87 % (12634)Instruction limit reached!
% 2.46/1.87 % (12634)------------------------------
% 2.46/1.87 % (12634)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.46/1.87 % (12634)Termination reason: Unknown
% 2.46/1.87 % (12634)Termination phase: Property scanning
% 2.46/1.87
% 2.46/1.87 % (12634)Memory used [KB]: 1791
% 2.46/1.87 % (12634)Time elapsed: 0.019 s
% 2.46/1.87 % (12634)Instructions burned: 64 (million)
% 2.46/1.87 % (12634)------------------------------
% 2.46/1.87 % (12634)------------------------------
% 2.46/1.88 % (12623)Instruction limit reached!
% 2.46/1.88 % (12623)------------------------------
% 2.46/1.88 % (12623)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.46/1.88 % (12623)Termination reason: Unknown
% 2.46/1.88 % (12623)Termination phase: Saturation
% 2.46/1.88
% 2.46/1.88 % (12623)Memory used [KB]: 6524
% 2.46/1.88 % (12623)Time elapsed: 0.107 s
% 2.46/1.88 % (12623)Instructions burned: 451 (million)
% 2.46/1.88 % (12623)------------------------------
% 2.46/1.88 % (12623)------------------------------
% 2.46/1.88 % (12635)Instruction limit reached!
% 2.46/1.88 % (12635)------------------------------
% 2.46/1.88 % (12635)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.46/1.88 % (12635)Termination reason: Unknown
% 2.46/1.88 % (12635)Termination phase: Property scanning
% 2.46/1.88
% 2.46/1.88 % (12635)Memory used [KB]: 1791
% 2.46/1.88 % (12635)Time elapsed: 0.011 s
% 2.46/1.88 % (12635)Instructions burned: 33 (million)
% 2.46/1.88 % (12635)------------------------------
% 2.46/1.88 % (12635)------------------------------
% 2.46/1.88 % (12636)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_12319 for (2995ds/96Mi)
% 2.46/1.89 % (12637)lrs+1002_1:4_au=on:cbe=off:cnfonf=lazy_pi_sigma_gen:hud=15:inj=on:nwc=4.0:s2a=on:sac=on:sp=reverse_arity:i=453:si=on:rtra=on_0 on DTF2THF_12319 for (2995ds/453Mi)
% 2.46/1.89 % (12638)lrs-1004_1:1_au=on:bsd=on:cbe=off:cnfonf=off:fe=axiom:fsd=on:i=71:si=on:rtra=on_0 on DTF2THF_12319 for (2995ds/71Mi)
% 2.46/1.90 % (12612)Instruction limit reached!
% 2.46/1.90 % (12612)------------------------------
% 2.46/1.90 % (12612)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.46/1.90 % (12612)Termination reason: Unknown
% 2.46/1.90 % (12612)Termination phase: Saturation
% 2.46/1.90
% 2.46/1.90 % (12612)Memory used [KB]: 8059
% 2.46/1.90 % (12612)Time elapsed: 0.321 s
% 2.46/1.90 % (12612)Instructions burned: 881 (million)
% 2.46/1.90 % (12612)------------------------------
% 2.46/1.90 % (12612)------------------------------
% 2.46/1.91 % (12636)Instruction limit reached!
% 2.46/1.91 % (12636)------------------------------
% 2.46/1.91 % (12636)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.46/1.91 % (12636)Termination reason: Unknown
% 2.46/1.91 % (12636)Termination phase: Saturation
% 2.46/1.91
% 2.46/1.91 % (12636)Memory used [KB]: 6652
% 2.46/1.91 % (12636)Time elapsed: 0.029 s
% 2.46/1.91 % (12636)Instructions burned: 96 (million)
% 2.46/1.91 % (12636)------------------------------
% 2.46/1.91 % (12636)------------------------------
% 2.46/1.91 % (12639)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_12319 for (2995ds/83Mi)
% 2.46/1.91 % (12638)Instruction limit reached!
% 2.46/1.91 % (12638)------------------------------
% 2.46/1.91 % (12638)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.46/1.91 % (12638)Termination reason: Unknown
% 2.46/1.91 % (12638)Termination phase: Saturation
% 2.46/1.91
% 2.46/1.91 % (12638)Memory used [KB]: 6396
% 2.46/1.91 % (12638)Time elapsed: 0.022 s
% 2.46/1.91 % (12638)Instructions burned: 73 (million)
% 2.46/1.91 % (12638)------------------------------
% 2.46/1.91 % (12638)------------------------------
% 2.46/1.92 % (12640)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_12319 for (2995ds/11Mi)
% 2.46/1.92 % (12641)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_gen_be_off:fsr=off:spb=non_intro:i=41:si=on:rtra=on_0 on DTF2THF_12319 for (2995ds/41Mi)
% 2.46/1.92 % (12640)Instruction limit reached!
% 2.46/1.92 % (12640)------------------------------
% 2.46/1.92 % (12640)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.46/1.92 % (12640)Termination reason: Unknown
% 2.46/1.92 % (12640)Termination phase: shuffling
% 2.46/1.92
% 2.46/1.92 % (12640)Memory used [KB]: 1407
% 2.46/1.92 % (12640)Time elapsed: 0.005 s
% 2.46/1.92 % (12640)Instructions burned: 12 (million)
% 2.46/1.92 % (12640)------------------------------
% 2.46/1.92 % (12640)------------------------------
% 2.46/1.93 % (12642)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_12319 for (2995ds/6Mi)
% 2.46/1.93 % (12641)Instruction limit reached!
% 2.46/1.93 % (12641)------------------------------
% 2.46/1.93 % (12641)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.46/1.93 % (12641)Termination reason: Unknown
% 2.46/1.93 % (12641)Termination phase: Property scanning
% 2.46/1.93
% 2.46/1.93 % (12641)Memory used [KB]: 1663
% 2.46/1.93 % (12641)Time elapsed: 0.013 s
% 2.46/1.93 % (12641)Instructions burned: 41 (million)
% 2.46/1.93 % (12641)------------------------------
% 2.46/1.93 % (12641)------------------------------
% 2.46/1.93 % (12639)Instruction limit reached!
% 2.46/1.93 % (12639)------------------------------
% 2.46/1.93 % (12639)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.46/1.93 % (12639)Termination reason: Unknown
% 2.46/1.93 % (12639)Termination phase: Saturation
% 2.46/1.93
% 2.46/1.93 % (12639)Memory used [KB]: 6396
% 2.46/1.93 % (12639)Time elapsed: 0.025 s
% 2.46/1.93 % (12639)Instructions burned: 86 (million)
% 2.46/1.93 % (12639)------------------------------
% 2.46/1.93 % (12639)------------------------------
% 2.46/1.93 % (12642)Instruction limit reached!
% 2.46/1.93 % (12642)------------------------------
% 2.46/1.93 % (12642)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.46/1.93 % (12642)Termination reason: Unknown
% 2.46/1.93 % (12642)Termination phase: shuffling
% 2.46/1.93
% 2.46/1.93 % (12642)Memory used [KB]: 1279
% 2.46/1.93 % (12642)Time elapsed: 0.003 s
% 2.46/1.93 % (12642)Instructions burned: 6 (million)
% 2.46/1.93 % (12642)------------------------------
% 2.46/1.93 % (12642)------------------------------
% 2.46/1.94 % (12643)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_12319 for (2995ds/150Mi)
% 2.46/1.94 % (12644)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_12319 for (2995ds/343Mi)
% 2.46/1.94 % (12645)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=109:si=on:rtra=on_0 on DTF2THF_12319 for (2995ds/109Mi)
% 2.46/1.95 % (12626)Instruction limit reached!
% 2.46/1.95 % (12626)------------------------------
% 2.46/1.95 % (12626)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.46/1.95 % (12626)Termination reason: Unknown
% 2.46/1.95 % (12626)Termination phase: Saturation
% 2.46/1.95
% 2.46/1.95 % (12626)Memory used [KB]: 7419
% 2.46/1.95 % (12626)Time elapsed: 0.160 s
% 2.46/1.95 % (12626)Instructions burned: 507 (million)
% 2.46/1.95 % (12626)------------------------------
% 2.46/1.95 % (12626)------------------------------
% 2.46/1.95 % (12633)Instruction limit reached!
% 2.46/1.95 % (12633)------------------------------
% 2.46/1.95 % (12633)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.46/1.95 % (12633)Termination reason: Unknown
% 2.46/1.95 % (12633)Termination phase: Saturation
% 2.46/1.95
% 2.46/1.95 % (12633)Memory used [KB]: 2942
% 2.46/1.95 % (12633)Time elapsed: 0.108 s
% 2.46/1.95 % (12633)Instructions burned: 434 (million)
% 2.46/1.95 % (12633)------------------------------
% 2.46/1.95 % (12633)------------------------------
% 2.46/1.96 % (12646)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=253:si=on:rtra=on_0 on DTF2THF_12319 for (2995ds/253Mi)
% 2.46/1.96 % (12647)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_12319 for (2995ds/140Mi)
% 2.46/1.97 % (12645)Instruction limit reached!
% 2.46/1.97 % (12645)------------------------------
% 2.46/1.97 % (12645)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.46/1.97 % (12645)Termination reason: Unknown
% 2.46/1.97 % (12645)Termination phase: Saturation
% 2.46/1.97
% 2.46/1.97 % (12645)Memory used [KB]: 6780
% 2.46/1.97 % (12645)Time elapsed: 0.030 s
% 2.46/1.97 % (12645)Instructions burned: 111 (million)
% 2.46/1.97 % (12645)------------------------------
% 2.46/1.97 % (12645)------------------------------
% 2.46/1.98 % (12648)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=614:si=on:rtra=on_0 on DTF2THF_12319 for (2994ds/614Mi)
% 2.46/1.99 % (12643)Instruction limit reached!
% 2.46/1.99 % (12643)------------------------------
% 2.46/1.99 % (12643)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.46/1.99 % (12643)Termination reason: Unknown
% 2.46/1.99 % (12643)Termination phase: Saturation
% 2.46/1.99
% 2.46/1.99 % (12643)Memory used [KB]: 7803
% 2.46/1.99 % (12643)Time elapsed: 0.046 s
% 2.46/1.99 % (12643)Instructions burned: 152 (million)
% 2.46/1.99 % (12643)------------------------------
% 2.46/1.99 % (12643)------------------------------
% 2.46/2.00 % (12649)lrs+1002_1:1_e2e=on:fde=unused:fe=axiom:prag=on:sd=1:sos=on:ss=axioms:st=2.0:i=202:si=on:rtra=on_0 on DTF2THF_12319 for (2994ds/202Mi)
% 2.46/2.00 % (12637)Instruction limit reached!
% 2.46/2.00 % (12637)------------------------------
% 2.46/2.00 % (12637)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.46/2.00 % (12637)Termination reason: Unknown
% 2.46/2.00 % (12637)Termination phase: Saturation
% 2.46/2.00
% 2.46/2.00 % (12637)Memory used [KB]: 6524
% 2.46/2.00 % (12637)Time elapsed: 0.110 s
% 2.46/2.00 % (12637)Instructions burned: 453 (million)
% 2.46/2.00 % (12637)------------------------------
% 2.46/2.00 % (12637)------------------------------
% 2.46/2.00 % (12647)Instruction limit reached!
% 2.46/2.00 % (12647)------------------------------
% 2.46/2.00 % (12647)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.46/2.00 % (12647)Termination reason: Unknown
% 2.46/2.00 % (12647)Termination phase: Saturation
% 2.46/2.00
% 2.46/2.00 % (12647)Memory used [KB]: 6524
% 2.46/2.00 % (12647)Time elapsed: 0.061 s
% 2.46/2.00 % (12647)Instructions burned: 141 (million)
% 2.46/2.00 % (12647)------------------------------
% 2.46/2.00 % (12647)------------------------------
% 2.46/2.01 % (12650)dis+1002_1:1_au=on:cs=on:ins=3:kws=inv_frequency:nwc=10.0:ss=axioms:st=3.0:i=339:si=on:rtra=on_0 on DTF2THF_12319 for (2994ds/339Mi)
% 6.22/2.01 % (12651)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=283:si=on:rtra=on_0 on DTF2THF_12319 for (2994ds/283Mi)
% 6.22/2.03 % (12646)Instruction limit reached!
% 6.22/2.03 % (12646)------------------------------
% 6.22/2.03 % (12646)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.22/2.03 % (12646)Termination reason: Unknown
% 6.22/2.03 % (12646)Termination phase: Saturation
% 6.22/2.03
% 6.22/2.03 % (12646)Memory used [KB]: 8187
% 6.22/2.03 % (12646)Time elapsed: 0.079 s
% 6.22/2.03 % (12646)Instructions burned: 254 (million)
% 6.22/2.03 % (12646)------------------------------
% 6.22/2.03 % (12646)------------------------------
% 6.22/2.04 % (12644)Instruction limit reached!
% 6.22/2.04 % (12644)------------------------------
% 6.22/2.04 % (12644)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.22/2.04 % (12644)Termination reason: Unknown
% 6.22/2.04 % (12644)Termination phase: Saturation
% 6.22/2.04
% 6.22/2.04 % (12644)Memory used [KB]: 7547
% 6.22/2.04 % (12644)Time elapsed: 0.101 s
% 6.22/2.04 % (12644)Instructions burned: 343 (million)
% 6.22/2.04 % (12644)------------------------------
% 6.22/2.04 % (12644)------------------------------
% 6.22/2.04 % (12652)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_12319 for (2994ds/134Mi)
% 6.22/2.05 % (12653)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_12319 for (2994ds/298Mi)
% 6.22/2.06 % (12649)Instruction limit reached!
% 6.22/2.06 % (12649)------------------------------
% 6.22/2.06 % (12649)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.22/2.06 % (12649)Termination reason: Unknown
% 6.22/2.06 % (12649)Termination phase: Saturation
% 6.22/2.06
% 6.22/2.06 % (12649)Memory used [KB]: 8315
% 6.22/2.06 % (12649)Time elapsed: 0.062 s
% 6.22/2.06 % (12649)Instructions burned: 202 (million)
% 6.22/2.06 % (12649)------------------------------
% 6.22/2.06 % (12649)------------------------------
% 6.22/2.07 % (12654)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_12319 for (2993ds/192Mi)
% 6.22/2.08 % (12652)Instruction limit reached!
% 6.22/2.08 % (12652)------------------------------
% 6.22/2.08 % (12652)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.22/2.08 % (12652)Termination reason: Unknown
% 6.22/2.08 % (12652)Termination phase: Saturation
% 6.22/2.08
% 6.22/2.08 % (12652)Memory used [KB]: 7036
% 6.22/2.08 % (12652)Time elapsed: 0.037 s
% 6.22/2.08 % (12652)Instructions burned: 136 (million)
% 6.22/2.08 % (12652)------------------------------
% 6.22/2.08 % (12652)------------------------------
% 6.22/2.08 % (12651)Instruction limit reached!
% 6.22/2.08 % (12651)------------------------------
% 6.22/2.08 % (12651)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.22/2.08 % (12651)Termination reason: Unknown
% 6.22/2.08 % (12651)Termination phase: Saturation
% 6.22/2.08
% 6.22/2.08 % (12651)Memory used [KB]: 8827
% 6.22/2.08 % (12651)Time elapsed: 0.093 s
% 6.22/2.08 % (12651)Instructions burned: 286 (million)
% 6.22/2.08 % (12651)------------------------------
% 6.22/2.08 % (12651)------------------------------
% 6.22/2.09 % (12655)lrs+10_1:1_bd=off:hud=1:nm=0:prag=on:sd=2:sgt=32:sos=all:ss=axioms:i=258:si=on:rtra=on_0 on DTF2THF_12319 for (2993ds/258Mi)
% 6.22/2.09 % (12656)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on DTF2THF_12319 for (2993ds/90Mi)
% 6.22/2.10 % (12650)Instruction limit reached!
% 6.22/2.10 % (12650)------------------------------
% 6.22/2.10 % (12650)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.22/2.10 % (12650)Termination reason: Unknown
% 6.22/2.10 % (12650)Termination phase: Saturation
% 6.22/2.10
% 6.22/2.10 % (12650)Memory used [KB]: 7291
% 6.22/2.10 % (12650)Time elapsed: 0.099 s
% 6.22/2.10 % (12650)Instructions burned: 339 (million)
% 6.22/2.10 % (12650)------------------------------
% 6.22/2.10 % (12650)------------------------------
% 6.78/2.11 % (12657)dis+1004_16:1_avsq=on:avsqr=1,16:cnfonf=lazy_gen:cs=on:fe=off:tgt=ground:tnu=1:i=231:si=on:rtra=on_0 on DTF2THF_12319 for (2993ds/231Mi)
% 6.78/2.12 % (12656)Instruction limit reached!
% 6.78/2.12 % (12656)------------------------------
% 6.78/2.12 % (12656)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.78/2.12 % (12656)Termination reason: Unknown
% 6.78/2.12 % (12656)Termination phase: Saturation
% 6.78/2.12
% 6.78/2.12 % (12656)Memory used [KB]: 6908
% 6.78/2.12 % (12656)Time elapsed: 0.025 s
% 6.78/2.12 % (12656)Instructions burned: 92 (million)
% 6.78/2.12 % (12656)------------------------------
% 6.78/2.12 % (12656)------------------------------
% 6.78/2.12 % (12654)Instruction limit reached!
% 6.78/2.12 % (12654)------------------------------
% 6.78/2.12 % (12654)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.78/2.12 % (12654)Termination reason: Unknown
% 6.78/2.12 % (12654)Termination phase: Saturation
% 6.78/2.12
% 6.78/2.12 % (12654)Memory used [KB]: 7291
% 6.78/2.12 % (12654)Time elapsed: 0.054 s
% 6.78/2.12 % (12654)Instructions burned: 192 (million)
% 6.78/2.12 % (12654)------------------------------
% 6.78/2.12 % (12654)------------------------------
% 6.78/2.12 % (12658)lrs+1002_1:1_au=on:s2a=on:sgt=32:slsq=on:slsqc=1:slsql=off:ss=axioms:i=458:si=on:rtra=on_0 on DTF2THF_12319 for (2993ds/458Mi)
% 6.78/2.13 % (12653)Instruction limit reached!
% 6.78/2.13 % (12653)------------------------------
% 6.78/2.13 % (12653)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.78/2.13 % (12653)Termination reason: Unknown
% 6.78/2.13 % (12653)Termination phase: Saturation
% 6.78/2.13
% 6.78/2.13 % (12653)Memory used [KB]: 6524
% 6.78/2.13 % (12653)Time elapsed: 0.076 s
% 6.78/2.13 % (12653)Instructions burned: 301 (million)
% 6.78/2.13 % (12653)------------------------------
% 6.78/2.13 % (12653)------------------------------
% 6.78/2.13 % (12659)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_12319 for (2993ds/31Mi)
% 6.78/2.13 % (12660)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:s2a=on:sp=weighted_frequency:ss=axioms:i=297:si=on:rtra=on_0 on DTF2THF_12319 for (2993ds/297Mi)
% 6.78/2.14 % (12659)Instruction limit reached!
% 6.78/2.14 % (12659)------------------------------
% 6.78/2.14 % (12659)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.78/2.14 % (12659)Termination reason: Unknown
% 6.78/2.14 % (12659)Termination phase: Property scanning
% 6.78/2.14
% 6.78/2.14 % (12659)Memory used [KB]: 1791
% 6.78/2.14 % (12659)Time elapsed: 0.010 s
% 6.78/2.14 % (12659)Instructions burned: 34 (million)
% 6.78/2.14 % (12659)------------------------------
% 6.78/2.14 % (12659)------------------------------
% 6.78/2.15 % (12661)dis+2_1:4_amm=off:au=on:cbe=off:cnfonf=lazy_gen:hfaw=0:hfsq=on:hfsql=off:plsq=on:plsqc=1:plsqr=35,4:sac=on:i=987:si=on:rtra=on_0 on DTF2THF_12319 for (2993ds/987Mi)
% 6.78/2.16 % (12630)Instruction limit reached!
% 6.78/2.16 % (12630)------------------------------
% 6.78/2.16 % (12630)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.78/2.16 % (12630)Termination reason: Unknown
% 6.78/2.16 % (12630)Termination phase: Saturation
% 6.78/2.16
% 6.78/2.16 % (12630)Memory used [KB]: 10234
% 6.78/2.16 % (12630)Time elapsed: 0.344 s
% 6.78/2.16 % (12630)Instructions burned: 1089 (million)
% 6.78/2.16 % (12630)------------------------------
% 6.78/2.16 % (12630)------------------------------
% 6.78/2.16 % (12655)Instruction limit reached!
% 6.78/2.16 % (12655)------------------------------
% 6.78/2.16 % (12655)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.78/2.16 % (12655)Termination reason: Unknown
% 6.78/2.16 % (12655)Termination phase: Saturation
% 6.78/2.16
% 6.78/2.16 % (12655)Memory used [KB]: 7547
% 6.78/2.16 % (12655)Time elapsed: 0.076 s
% 6.78/2.16 % (12655)Instructions burned: 259 (million)
% 6.78/2.16 % (12655)------------------------------
% 6.78/2.16 % (12655)------------------------------
% 6.78/2.17 % (12662)lrs+10_1:1024_avsq=on:avsqc=4:avsqr=584411,1048576:bd=off:bet=on:br=off:chr=on:fsd=on:fsdmm=1:hud=10:nm=0:ntd=on:nwc=9.0:piset=or:plsq=on:plsqc=2:plsql=on:plsqr=852219,1048576:rawr=on:sp=const_frequency:spb=units:i=182:si=on:rtra=on_0 on DTF2THF_12319 for (2992ds/182Mi)
% 6.78/2.17 % (12663)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=182:si=on:rtra=on_0 on DTF2THF_12319 for (2992ds/182Mi)
% 6.78/2.18 % (12657)Instruction limit reached!
% 6.78/2.18 % (12657)------------------------------
% 6.78/2.18 % (12657)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.78/2.18 % (12657)Termination reason: Unknown
% 6.78/2.18 % (12657)Termination phase: Saturation
% 6.78/2.18
% 6.78/2.18 % (12657)Memory used [KB]: 10490
% 6.78/2.18 % (12657)Time elapsed: 0.067 s
% 6.78/2.18 % (12657)Instructions burned: 233 (million)
% 6.78/2.18 % (12657)------------------------------
% 6.78/2.18 % (12657)------------------------------
% 6.78/2.19 % (12664)dis+10_1:8_cha=on:cnfonf=lazy_pi_sigma_gen:fe=axiom:hud=5:plsq=on:plsqr=32,1:prag=on:sos=all:i=154:si=on:rtra=on_0 on DTF2THF_12319 for (2992ds/154Mi)
% 7.29/2.21 % (12660)Instruction limit reached!
% 7.29/2.21 % (12660)------------------------------
% 7.29/2.21 % (12660)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.29/2.21 % (12660)Termination reason: Unknown
% 7.29/2.21 % (12660)Termination phase: Saturation
% 7.29/2.21
% 7.29/2.21 % (12660)Memory used [KB]: 8187
% 7.29/2.21 % (12660)Time elapsed: 0.074 s
% 7.29/2.21 % (12660)Instructions burned: 297 (million)
% 7.29/2.21 % (12660)------------------------------
% 7.29/2.21 % (12660)------------------------------
% 7.29/2.22 % (12665)dis+1003_1:64_atotf=0.4:au=on:fsr=off:hflw=5:hfsq=on:hfsqc=20:hfsql=off:plsq=on:plsqc=1:plsqr=32,1:i=79:si=on:rtra=on_0 on DTF2THF_12319 for (2992ds/79Mi)
% 7.29/2.22 % (12662)Instruction limit reached!
% 7.29/2.22 % (12662)------------------------------
% 7.29/2.22 % (12662)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.29/2.22 % (12662)Termination reason: Unknown
% 7.29/2.22 % (12662)Termination phase: Saturation
% 7.29/2.22
% 7.29/2.22 % (12662)Memory used [KB]: 7164
% 7.29/2.22 % (12662)Time elapsed: 0.053 s
% 7.29/2.22 % (12662)Instructions burned: 183 (million)
% 7.29/2.22 % (12662)------------------------------
% 7.29/2.22 % (12662)------------------------------
% 7.29/2.23 % (12664)Instruction limit reached!
% 7.29/2.23 % (12664)------------------------------
% 7.29/2.23 % (12664)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.29/2.23 % (12664)Termination reason: Unknown
% 7.29/2.23 % (12664)Termination phase: Saturation
% 7.29/2.23
% 7.29/2.23 % (12664)Memory used [KB]: 6524
% 7.29/2.23 % (12664)Time elapsed: 0.041 s
% 7.29/2.23 % (12664)Instructions burned: 158 (million)
% 7.29/2.23 % (12664)------------------------------
% 7.29/2.23 % (12664)------------------------------
% 7.29/2.23 % (12663)Instruction limit reached!
% 7.29/2.23 % (12663)------------------------------
% 7.29/2.23 % (12663)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.29/2.23 % (12663)Termination reason: Unknown
% 7.29/2.23 % (12663)Termination phase: Saturation
% 7.29/2.23
% 7.29/2.23 % (12663)Memory used [KB]: 9210
% 7.29/2.23 % (12663)Time elapsed: 0.057 s
% 7.29/2.23 % (12663)Instructions burned: 182 (million)
% 7.29/2.23 % (12663)------------------------------
% 7.29/2.23 % (12663)------------------------------
% 7.29/2.23 % (12666)dis+1010_5:2_anc=all_dependent:awrs=converge:bd=off:bet=on:c=on:cha=on:cnfonf=lazy_not_gen_be_off:fe=axiom:hud=5:kws=precedence:piset=and:prag=on:s2a=on:sac=on:slsq=on:slsqc=1:sp=reverse_arity:ss=axioms:st=1.5:i=216:si=on:rtra=on_0 on DTF2THF_12319 for (2992ds/216Mi)
% 7.29/2.23 % (12648)Instruction limit reached!
% 7.29/2.23 % (12648)------------------------------
% 7.29/2.23 % (12648)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.29/2.23 % (12648)Termination reason: Unknown
% 7.29/2.23 % (12648)Termination phase: Saturation
% 7.29/2.23
% 7.29/2.23 % (12648)Memory used [KB]: 8187
% 7.29/2.23 % (12648)Time elapsed: 0.274 s
% 7.29/2.23 % (12648)Instructions burned: 616 (million)
% 7.29/2.23 % (12648)------------------------------
% 7.29/2.23 % (12648)------------------------------
% 7.29/2.24 % (12665)Instruction limit reached!
% 7.29/2.24 % (12665)------------------------------
% 7.29/2.24 % (12665)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.29/2.24 % (12665)Termination reason: Unknown
% 7.29/2.24 % (12665)Termination phase: Saturation
% 7.29/2.24
% 7.29/2.24 % (12665)Memory used [KB]: 6396
% 7.29/2.24 % (12665)Time elapsed: 0.022 s
% 7.29/2.24 % (12665)Instructions burned: 80 (million)
% 7.29/2.24 % (12665)------------------------------
% 7.29/2.24 % (12665)------------------------------
% 7.29/2.24 % (12667)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_12319 for (2992ds/114Mi)
% 7.29/2.24 % (12668)dis+1002_1:1_acc=on:au=on:bd=off:e2e=on:sgt=8:ss=axioms:i=922:si=on:rtra=on_0 on DTF2THF_12319 for (2992ds/922Mi)
% 7.29/2.24 % (12669)lrs+10_1:128_au=on:bd=off:cnfonf=lazy_not_gen_be_off:nwc=10.0:piset=and:i=182:si=on:rtra=on_0 on DTF2THF_12319 for (2992ds/182Mi)
% 7.29/2.25 % (12670)ott+1010_1:1024_au=on:av=off:c=on:cnfonf=conj_eager:piset=equals:s2a=on:sp=occurrence:spb=units:ss=axioms:i=164:si=on:rtra=on_0 on DTF2THF_12319 for (2992ds/164Mi)
% 7.29/2.26 % (12658)Instruction limit reached!
% 7.29/2.26 % (12658)------------------------------
% 7.29/2.26 % (12658)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.29/2.26 % (12658)Termination reason: Unknown
% 7.29/2.26 % (12658)Termination phase: Saturation
% 7.29/2.26
% 7.29/2.26 % (12658)Memory used [KB]: 7803
% 7.29/2.26 % (12658)Time elapsed: 0.141 s
% 7.29/2.26 % (12658)Instructions burned: 458 (million)
% 7.29/2.26 % (12658)------------------------------
% 7.29/2.26 % (12658)------------------------------
% 7.29/2.27 % (12667)Instruction limit reached!
% 7.29/2.27 % (12667)------------------------------
% 7.29/2.27 % (12667)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.29/2.27 % (12667)Termination reason: Unknown
% 7.29/2.27 % (12667)Termination phase: Saturation
% 7.29/2.27
% 7.29/2.27 % (12667)Memory used [KB]: 6780
% 7.29/2.27 % (12667)Time elapsed: 0.032 s
% 7.29/2.27 % (12667)Instructions burned: 116 (million)
% 7.29/2.27 % (12667)------------------------------
% 7.29/2.27 % (12667)------------------------------
% 7.29/2.27 % (12671)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=50:si=on:rtra=on_0 on DTF2THF_12319 for (2991ds/50Mi)
% 7.29/2.28 % (12672)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_12319 for (2991ds/368Mi)
% 7.29/2.28 % (12666)Instruction limit reached!
% 7.29/2.28 % (12666)------------------------------
% 7.29/2.28 % (12666)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.29/2.28 % (12666)Termination reason: Unknown
% 7.29/2.28 % (12666)Termination phase: Saturation
% 7.29/2.28
% 7.29/2.28 % (12666)Memory used [KB]: 6524
% 7.29/2.28 % (12666)Time elapsed: 0.054 s
% 7.29/2.28 % (12666)Instructions burned: 217 (million)
% 7.29/2.28 % (12666)------------------------------
% 7.29/2.28 % (12666)------------------------------
% 7.29/2.29 % (12671)Instruction limit reached!
% 7.29/2.29 % (12671)------------------------------
% 7.29/2.29 % (12671)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.29/2.29 % (12671)Termination reason: Unknown
% 7.29/2.29 % (12671)Termination phase: Function definition elimination
% 7.29/2.29
% 7.29/2.29 % (12671)Memory used [KB]: 1663
% 7.29/2.29 % (12671)Time elapsed: 0.014 s
% 7.29/2.29 % (12671)Instructions burned: 50 (million)
% 7.29/2.29 % (12671)------------------------------
% 7.29/2.29 % (12671)------------------------------
% 7.29/2.29 % (12669)Instruction limit reached!
% 7.29/2.29 % (12669)------------------------------
% 7.29/2.29 % (12669)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.29/2.29 % (12669)Termination reason: Unknown
% 7.29/2.29 % (12669)Termination phase: Saturation
% 7.29/2.29
% 7.29/2.29 % (12669)Memory used [KB]: 6524
% 7.29/2.29 % (12669)Time elapsed: 0.049 s
% 7.29/2.29 % (12669)Instructions burned: 184 (million)
% 7.29/2.29 % (12669)------------------------------
% 7.29/2.29 % (12669)------------------------------
% 7.29/2.29 % (12673)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=1021:si=on:rtra=on_0 on DTF2THF_12319 for (2991ds/1021Mi)
% 7.29/2.29 % (12670)Instruction limit reached!
% 7.29/2.29 % (12670)------------------------------
% 7.29/2.29 % (12670)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.29/2.29 % (12670)Termination reason: Unknown
% 7.29/2.29 % (12670)Termination phase: Saturation
% 7.29/2.29
% 7.29/2.29 % (12670)Memory used [KB]: 2302
% 7.29/2.29 % (12670)Time elapsed: 0.047 s
% 7.29/2.29 % (12670)Instructions burned: 164 (million)
% 7.29/2.29 % (12670)------------------------------
% 7.29/2.29 % (12670)------------------------------
% 8.02/2.30 % (12674)dis+10_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=267:si=on:rtra=on_0 on DTF2THF_12319 for (2991ds/267Mi)
% 8.02/2.30 % (12675)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=204:si=on:rtra=on_0 on DTF2THF_12319 for (2991ds/204Mi)
% 8.02/2.30 % (12676)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_12319 for (2991ds/26Mi)
% 8.02/2.31 % (12676)Instruction limit reached!
% 8.02/2.31 % (12676)------------------------------
% 8.02/2.31 % (12676)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.02/2.31 % (12676)Termination reason: Unknown
% 8.02/2.31 % (12676)Termination phase: Property scanning
% 8.02/2.31
% 8.02/2.31 % (12676)Memory used [KB]: 1663
% 8.02/2.31 % (12676)Time elapsed: 0.008 s
% 8.02/2.31 % (12676)Instructions burned: 27 (million)
% 8.02/2.31 % (12676)------------------------------
% 8.02/2.31 % (12676)------------------------------
% 8.02/2.32 % (12677)dis+1002_1:1_bd=preordered:c=on:cbe=off:cnfonf=lazy_not_gen_be_off:hud=10:ixr=off:prag=on:i=53:si=on:rtra=on_0 on DTF2THF_12319 for (2991ds/53Mi)
% 8.02/2.33 % (12677)Instruction limit reached!
% 8.02/2.33 % (12677)------------------------------
% 8.02/2.33 % (12677)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.02/2.33 % (12677)Termination reason: Unknown
% 8.02/2.33 % (12677)Termination phase: Property scanning
% 8.02/2.33
% 8.02/2.33 % (12677)Memory used [KB]: 1791
% 8.02/2.33 % (12677)Time elapsed: 0.015 s
% 8.02/2.33 % (12677)Instructions burned: 57 (million)
% 8.02/2.33 % (12677)------------------------------
% 8.02/2.33 % (12677)------------------------------
% 8.02/2.34 % (12678)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=4436:si=on:rtra=on_0 on DTF2THF_12319 for (2991ds/4436Mi)
% 8.02/2.36 % (12675)Instruction limit reached!
% 8.02/2.36 % (12675)------------------------------
% 8.02/2.36 % (12675)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.02/2.36 % (12675)Termination reason: Unknown
% 8.02/2.36 % (12675)Termination phase: Saturation
% 8.02/2.36
% 8.02/2.36 % (12675)Memory used [KB]: 7291
% 8.02/2.36 % (12675)Time elapsed: 0.064 s
% 8.02/2.36 % (12675)Instructions burned: 206 (million)
% 8.02/2.36 % (12675)------------------------------
% 8.02/2.36 % (12675)------------------------------
% 8.02/2.36 % (12674)Instruction limit reached!
% 8.02/2.36 % (12674)------------------------------
% 8.02/2.36 % (12674)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.02/2.36 % (12674)Termination reason: Unknown
% 8.02/2.36 % (12674)Termination phase: Saturation
% 8.02/2.36
% 8.02/2.36 % (12674)Memory used [KB]: 8699
% 8.02/2.36 % (12674)Time elapsed: 0.067 s
% 8.02/2.36 % (12674)Instructions burned: 267 (million)
% 8.02/2.36 % (12674)------------------------------
% 8.02/2.36 % (12674)------------------------------
% 8.02/2.37 % (12679)dis+1010_1:1_acc=model:avsq=on:ixr=off:prag=on:s2a=on:sac=on:i=1539:si=on:rtra=on_0 on DTF2THF_12319 for (2991ds/1539Mi)
% 8.02/2.37 % (12680)lrs+2_1:1_bd=off:e2e=on:fde=none:kws=inv_precedence:plsq=on:plsqr=32,1:sos=on:i=408:si=on:rtra=on_0 on DTF2THF_12319 for (2991ds/408Mi)
% 8.02/2.38 % (12672)Instruction limit reached!
% 8.02/2.38 % (12672)------------------------------
% 8.02/2.38 % (12672)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.02/2.38 % (12672)Termination reason: Unknown
% 8.02/2.38 % (12672)Termination phase: Saturation
% 8.02/2.38
% 8.02/2.38 % (12672)Memory used [KB]: 7419
% 8.02/2.38 % (12672)Time elapsed: 0.098 s
% 8.02/2.38 % (12672)Instructions burned: 372 (million)
% 8.02/2.38 % (12672)------------------------------
% 8.02/2.38 % (12672)------------------------------
% 8.02/2.39 % (12661)Instruction limit reached!
% 8.02/2.39 % (12661)------------------------------
% 8.02/2.39 % (12661)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.02/2.39 % (12661)Termination reason: Unknown
% 8.02/2.39 % (12661)Termination phase: Saturation
% 8.02/2.39
% 8.02/2.39 % (12661)Memory used [KB]: 9083
% 8.02/2.39 % (12661)Time elapsed: 0.240 s
% 8.02/2.39 % (12661)Instructions burned: 989 (million)
% 8.02/2.39 % (12661)------------------------------
% 8.02/2.39 % (12661)------------------------------
% 8.02/2.39 % (12681)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=5205:si=on:rtra=on_0 on DTF2THF_12319 for (2990ds/5205Mi)
% 8.02/2.40 % (12682)dis+1010_1:4_au=on:av=off:cbe=off:nwc=10.0:s2a=on:s2at=3.0:sd=2:ss=axioms:st=5.0:i=1913:si=on:rtra=on_0 on DTF2THF_12319 for (2990ds/1913Mi)
% 8.56/2.50 % (12680)Instruction limit reached!
% 8.56/2.50 % (12680)------------------------------
% 8.56/2.50 % (12680)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.56/2.50 % (12680)Termination reason: Unknown
% 8.56/2.50 % (12680)Termination phase: Saturation
% 8.56/2.50
% 8.56/2.50 % (12680)Memory used [KB]: 9210
% 8.56/2.50 % (12680)Time elapsed: 0.131 s
% 8.56/2.50 % (12680)Instructions burned: 409 (million)
% 8.56/2.50 % (12680)------------------------------
% 8.56/2.50 % (12680)------------------------------
% 8.56/2.51 % (12683)lrs+2_1:1_bd=off:cbe=off:piset=equals:sd=1:sgt=20:sos=all:ss=axioms:i=4350:si=on:rtra=on_0 on DTF2THF_12319 for (2989ds/4350Mi)
% 8.56/2.53 % (12668)Instruction limit reached!
% 8.56/2.53 % (12668)------------------------------
% 8.56/2.53 % (12668)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.56/2.53 % (12668)Termination reason: Unknown
% 8.56/2.53 % (12668)Termination phase: Saturation
% 8.56/2.53
% 8.56/2.53 % (12668)Memory used [KB]: 9338
% 8.56/2.53 % (12668)Time elapsed: 0.294 s
% 8.56/2.53 % (12668)Instructions burned: 922 (million)
% 8.56/2.53 % (12668)------------------------------
% 8.56/2.53 % (12668)------------------------------
% 8.56/2.54 % (12684)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=68:si=on:rtra=on_0 on DTF2THF_12319 for (2989ds/68Mi)
% 8.56/2.56 % (12684)Instruction limit reached!
% 8.56/2.56 % (12684)------------------------------
% 8.56/2.56 % (12684)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.56/2.56 % (12684)Termination reason: Unknown
% 8.56/2.56 % (12684)Termination phase: Property scanning
% 8.56/2.56
% 8.56/2.56 % (12684)Memory used [KB]: 1791
% 8.56/2.56 % (12684)Time elapsed: 0.019 s
% 8.56/2.56 % (12684)Instructions burned: 71 (million)
% 8.56/2.56 % (12684)------------------------------
% 8.56/2.56 % (12684)------------------------------
% 8.56/2.57 % (12685)dis+10_1:1_au=on:nwc=5.0:s2a=on:s2at=2.0:sac=on:sd=7:ss=axioms:st=2.0:i=358:si=on:rtra=on_0 on DTF2THF_12319 for (2989ds/358Mi)
% 9.03/2.62 % (12673)Instruction limit reached!
% 9.03/2.62 % (12673)------------------------------
% 9.03/2.62 % (12673)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.03/2.62 % (12673)Termination reason: Unknown
% 9.03/2.62 % (12673)Termination phase: Saturation
% 9.03/2.62
% 9.03/2.62 % (12673)Memory used [KB]: 9594
% 9.03/2.62 % (12673)Time elapsed: 0.326 s
% 9.03/2.62 % (12673)Instructions burned: 1022 (million)
% 9.03/2.62 % (12673)------------------------------
% 9.03/2.62 % (12673)------------------------------
% 9.03/2.63 % (12686)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_12319 for (2988ds/31Mi)
% 9.03/2.64 % (12686)Instruction limit reached!
% 9.03/2.64 % (12686)------------------------------
% 9.03/2.64 % (12686)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.03/2.64 % (12686)Termination reason: Unknown
% 9.03/2.64 % (12686)Termination phase: Property scanning
% 9.03/2.64
% 9.03/2.64 % (12686)Memory used [KB]: 1791
% 9.03/2.64 % (12686)Time elapsed: 0.010 s
% 9.03/2.64 % (12686)Instructions burned: 31 (million)
% 9.03/2.64 % (12686)------------------------------
% 9.03/2.64 % (12686)------------------------------
% 9.03/2.65 % (12687)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_12319 for (2988ds/279Mi)
% 9.03/2.68 % (12685)Instruction limit reached!
% 9.03/2.68 % (12685)------------------------------
% 9.03/2.68 % (12685)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.03/2.68 % (12685)Termination reason: Unknown
% 9.03/2.68 % (12685)Termination phase: Saturation
% 9.03/2.68
% 9.03/2.68 % (12685)Memory used [KB]: 7547
% 9.03/2.68 % (12685)Time elapsed: 0.132 s
% 9.03/2.68 % (12685)Instructions burned: 358 (million)
% 9.03/2.68 % (12685)------------------------------
% 9.03/2.68 % (12685)------------------------------
% 9.03/2.69 % (12688)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_12319 for (2987ds/258Mi)
% 9.51/2.71 % (12687)Instruction limit reached!
% 9.51/2.71 % (12687)------------------------------
% 9.51/2.71 % (12687)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.51/2.71 % (12687)Termination reason: Unknown
% 9.51/2.71 % (12687)Termination phase: Saturation
% 9.51/2.71
% 9.51/2.71 % (12687)Memory used [KB]: 6524
% 9.51/2.71 % (12687)Time elapsed: 0.068 s
% 9.51/2.71 % (12687)Instructions burned: 281 (million)
% 9.51/2.71 % (12687)------------------------------
% 9.51/2.71 % (12687)------------------------------
% 9.51/2.72 % (12689)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_12319 for (2987ds/26Mi)
% 9.51/2.73 % (12689)Instruction limit reached!
% 9.51/2.73 % (12689)------------------------------
% 9.51/2.73 % (12689)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.51/2.73 % (12689)Termination reason: Unknown
% 9.51/2.73 % (12689)Termination phase: Property scanning
% 9.51/2.73
% 9.51/2.73 % (12689)Memory used [KB]: 1663
% 9.51/2.73 % (12689)Time elapsed: 0.008 s
% 9.51/2.73 % (12689)Instructions burned: 27 (million)
% 9.51/2.73 % (12689)------------------------------
% 9.51/2.73 % (12689)------------------------------
% 9.51/2.74 % (12690)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=995:si=on:rtra=on_0 on DTF2THF_12319 for (2987ds/995Mi)
% 9.51/2.76 % (12688)Instruction limit reached!
% 9.51/2.76 % (12688)------------------------------
% 9.51/2.76 % (12688)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.51/2.76 % (12688)Termination reason: Unknown
% 9.51/2.76 % (12688)Termination phase: Saturation
% 9.51/2.76
% 9.51/2.76 % (12688)Memory used [KB]: 7291
% 9.51/2.76 % (12688)Time elapsed: 0.071 s
% 9.51/2.76 % (12688)Instructions burned: 260 (million)
% 9.51/2.76 % (12688)------------------------------
% 9.51/2.76 % (12688)------------------------------
% 9.51/2.77 % (12691)dis+10_1:8_amm=sco:cbe=off:hflw=5:hfsq=on:hfsqc=14:hfsql=off:hfsqr=4,1:hud=5:ile=on:lma=on:nm=2:ntd=on:prag=on:sac=on:sp=frequency:i=373:si=on:rtra=on_0 on DTF2THF_12319 for (2986ds/373Mi)
% 9.67/2.87 % (12679)Instruction limit reached!
% 9.67/2.87 % (12679)------------------------------
% 9.67/2.87 % (12679)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.67/2.87 % (12679)Termination reason: Unknown
% 9.67/2.87 % (12679)Termination phase: Saturation
% 9.67/2.87
% 9.67/2.87 % (12679)Memory used [KB]: 8955
% 9.67/2.87 % (12679)Time elapsed: 0.496 s
% 9.67/2.87 % (12679)Instructions burned: 1541 (million)
% 9.67/2.87 % (12679)------------------------------
% 9.67/2.87 % (12679)------------------------------
% 9.67/2.88 % (12692)lrs+1010_1:128_au=on:cnfonf=lazy_pi_sigma_gen:hflw=4:hfsq=on:hfsqc=20:hfsql=off:i=253:si=on:rtra=on_0 on DTF2THF_12319 for (2985ds/253Mi)
% 9.67/2.88 % (12691)Instruction limit reached!
% 9.67/2.88 % (12691)------------------------------
% 9.67/2.88 % (12691)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.67/2.88 % (12691)Termination reason: Unknown
% 9.67/2.88 % (12691)Termination phase: Saturation
% 9.67/2.88
% 9.67/2.88 % (12691)Memory used [KB]: 7547
% 9.67/2.88 % (12691)Time elapsed: 0.118 s
% 9.67/2.88 % (12691)Instructions burned: 374 (million)
% 9.67/2.88 % (12691)------------------------------
% 9.67/2.88 % (12691)------------------------------
% 9.67/2.89 % (12693)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=832:si=on:rtra=on_0 on DTF2THF_12319 for (2985ds/832Mi)
% 10.32/2.94 % (12692)Instruction limit reached!
% 10.32/2.94 % (12692)------------------------------
% 10.32/2.94 % (12692)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.32/2.94 % (12692)Termination reason: Unknown
% 10.32/2.94 % (12692)Termination phase: Saturation
% 10.32/2.94
% 10.32/2.94 % (12692)Memory used [KB]: 6524
% 10.32/2.94 % (12692)Time elapsed: 0.063 s
% 10.32/2.94 % (12692)Instructions burned: 255 (million)
% 10.32/2.94 % (12692)------------------------------
% 10.32/2.94 % (12692)------------------------------
% 10.32/2.95 % (12694)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=668:si=on:rtra=on_0 on DTF2THF_12319 for (2985ds/668Mi)
% 10.32/2.97 % (12682)Instruction limit reached!
% 10.32/2.97 % (12682)------------------------------
% 10.32/2.97 % (12682)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.32/2.97 % (12682)Termination reason: Unknown
% 10.32/2.97 % (12682)Termination phase: Saturation
% 10.32/2.97
% 10.32/2.97 % (12682)Memory used [KB]: 4093
% 10.32/2.97 % (12682)Time elapsed: 0.601 s
% 10.32/2.97 % (12682)Instructions burned: 1914 (million)
% 10.32/2.97 % (12682)------------------------------
% 10.32/2.97 % (12682)------------------------------
% 10.32/2.98 % (12690)Instruction limit reached!
% 10.32/2.98 % (12690)------------------------------
% 10.32/2.98 % (12690)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.32/2.98 % (12690)Termination reason: Unknown
% 10.32/2.98 % (12690)Termination phase: Saturation
% 10.32/2.98
% 10.32/2.98 % (12690)Memory used [KB]: 8955
% 10.32/2.98 % (12690)Time elapsed: 0.243 s
% 10.32/2.98 % (12690)Instructions burned: 996 (million)
% 10.32/2.98 % (12690)------------------------------
% 10.32/2.98 % (12690)------------------------------
% 10.32/2.98 % (12695)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=40:si=on:rtra=on_0 on DTF2THF_12319 for (2984ds/40Mi)
% 10.32/2.99 % (12696)lrs+1010_1:1_cnfonf=lazy_pi_sigma_gen:fd=off:ntd=on:sd=1:sgt=32:sos=on:ss=axioms:i=294:si=on:rtra=on_0 on DTF2THF_12319 for (2984ds/294Mi)
% 10.32/2.99 % (12695)Instruction limit reached!
% 10.32/2.99 % (12695)------------------------------
% 10.32/2.99 % (12695)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.32/2.99 % (12695)Termination reason: Unknown
% 10.32/2.99 % (12695)Termination phase: Property scanning
% 10.32/2.99
% 10.32/2.99 % (12695)Memory used [KB]: 1663
% 10.32/2.99 % (12695)Time elapsed: 0.012 s
% 10.32/2.99 % (12695)Instructions burned: 40 (million)
% 10.32/2.99 % (12695)------------------------------
% 10.32/2.99 % (12695)------------------------------
% 10.32/3.00 % (12697)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:plsq=on:plsqr=32,1:prag=on:i=187:si=on:rtra=on_0 on DTF2THF_12319 for (2984ds/187Mi)
% 13.32/3.06 % (12697)Instruction limit reached!
% 13.32/3.06 % (12697)------------------------------
% 13.32/3.06 % (12697)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.32/3.06 % (12697)Termination reason: Unknown
% 13.32/3.06 % (12697)Termination phase: Saturation
% 13.32/3.06
% 13.32/3.06 % (12697)Memory used [KB]: 7164
% 13.32/3.06 % (12697)Time elapsed: 0.053 s
% 13.32/3.06 % (12697)Instructions burned: 189 (million)
% 13.32/3.06 % (12697)------------------------------
% 13.32/3.06 % (12697)------------------------------
% 13.32/3.06 % (12696)Instruction limit reached!
% 13.32/3.06 % (12696)------------------------------
% 13.32/3.06 % (12696)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.32/3.06 % (12696)Termination reason: Unknown
% 13.32/3.06 % (12696)Termination phase: Saturation
% 13.32/3.06
% 13.32/3.06 % (12696)Memory used [KB]: 6524
% 13.32/3.06 % (12696)Time elapsed: 0.074 s
% 13.32/3.06 % (12696)Instructions burned: 294 (million)
% 13.32/3.06 % (12696)------------------------------
% 13.32/3.06 % (12696)------------------------------
% 13.32/3.07 % (12698)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_12319 for (2984ds/371Mi)
% 13.32/3.07 % (12699)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_12319 for (2983ds/1827Mi)
% 13.32/3.11 % (12694)Instruction limit reached!
% 13.32/3.11 % (12694)------------------------------
% 13.32/3.11 % (12694)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.32/3.11 % (12694)Termination reason: Unknown
% 13.32/3.11 % (12694)Termination phase: Saturation
% 13.32/3.11
% 13.32/3.11 % (12694)Memory used [KB]: 13432
% 13.32/3.11 % (12694)Time elapsed: 0.164 s
% 13.32/3.11 % (12694)Instructions burned: 670 (million)
% 13.32/3.11 % (12694)------------------------------
% 13.32/3.11 % (12694)------------------------------
% 13.32/3.12 % (12700)lrs+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:tnu=1:i=70:si=on:rtra=on_0 on DTF2THF_12319 for (2983ds/70Mi)
% 13.93/3.14 % (12700)Instruction limit reached!
% 13.93/3.14 % (12700)------------------------------
% 13.93/3.14 % (12700)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.93/3.14 % (12700)Termination reason: Unknown
% 13.93/3.14 % (12700)Termination phase: Saturation
% 13.93/3.14
% 13.93/3.14 % (12700)Memory used [KB]: 1791
% 13.93/3.14 % (12700)Time elapsed: 0.020 s
% 13.93/3.14 % (12700)Instructions burned: 73 (million)
% 13.93/3.14 % (12700)------------------------------
% 13.93/3.14 % (12700)------------------------------
% 13.93/3.15 % (12693)Instruction limit reached!
% 13.93/3.15 % (12693)------------------------------
% 13.93/3.15 % (12693)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.93/3.15 % (12693)Termination reason: Unknown
% 13.93/3.15 % (12693)Termination phase: Saturation
% 13.93/3.15
% 13.93/3.15 % (12693)Memory used [KB]: 8699
% 13.93/3.15 % (12693)Time elapsed: 0.257 s
% 13.93/3.15 % (12693)Instructions burned: 833 (million)
% 13.93/3.15 % (12693)------------------------------
% 13.93/3.15 % (12693)------------------------------
% 13.93/3.15 % (12701)lrs+10_1:20_bd=off:cnfonf=lazy_not_be_gen:fe=axiom:hud=10:ins=1:nm=20:prag=on:sos=on:i=316:si=on:rtra=on_0 on DTF2THF_12319 for (2983ds/316Mi)
% 13.93/3.16 % (12702)ott+1010_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=3548551,65536:s2a=on:i=932:si=on:rtra=on_0 on DTF2THF_12319 for (2983ds/932Mi)
% 13.93/3.18 % (12698)Instruction limit reached!
% 13.93/3.18 % (12698)------------------------------
% 13.93/3.18 % (12698)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.93/3.18 % (12698)Termination reason: Unknown
% 13.93/3.18 % (12698)Termination phase: Saturation
% 13.93/3.18
% 13.93/3.18 % (12698)Memory used [KB]: 7675
% 13.93/3.18 % (12698)Time elapsed: 0.137 s
% 13.93/3.18 % (12698)Instructions burned: 373 (million)
% 13.93/3.18 % (12698)------------------------------
% 13.93/3.18 % (12698)------------------------------
% 13.93/3.19 % (12703)lrs+1010_1:128_au=on:bd=preordered:cnfonf=lazy_pi_sigma_gen:plsq=on:plsqc=1:plsqr=32,1:sos=all:sp=occurrence:i=4714:si=on:rtra=on_0 on DTF2THF_12319 for (2982ds/4714Mi)
% 14.33/3.23 % (12701)Instruction limit reached!
% 14.33/3.23 % (12701)------------------------------
% 14.33/3.23 % (12701)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.33/3.23 % (12701)Termination reason: Unknown
% 14.33/3.23 % (12701)Termination phase: Saturation
% 14.33/3.23
% 14.33/3.23 % (12701)Memory used [KB]: 7291
% 14.33/3.23 % (12701)Time elapsed: 0.079 s
% 14.33/3.23 % (12701)Instructions burned: 318 (million)
% 14.33/3.23 % (12701)------------------------------
% 14.33/3.23 % (12701)------------------------------
% 14.33/3.24 % (12704)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=8250:si=on:rtra=on_0 on DTF2THF_12319 for (2982ds/8250Mi)
% 14.72/3.39 % (12702)Instruction limit reached!
% 14.72/3.39 % (12702)------------------------------
% 14.72/3.39 % (12702)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.72/3.39 % (12702)Termination reason: Unknown
% 14.72/3.39 % (12702)Termination phase: Saturation
% 14.72/3.39
% 14.72/3.39 % (12702)Memory used [KB]: 9594
% 14.72/3.39 % (12702)Time elapsed: 0.237 s
% 14.72/3.39 % (12702)Instructions burned: 934 (million)
% 14.72/3.39 % (12702)------------------------------
% 14.72/3.39 % (12702)------------------------------
% 15.27/3.40 % (12705)lrs+1002_1:1_apa=on:cnfonf=off:fd=off:flr=on:hud=1:lcm=reverse:prag=on:sd=1:sos=on:ss=axioms:i=770:si=on:rtra=on_0 on DTF2THF_12319 for (2980ds/770Mi)
% 15.87/3.62 % (12705)Instruction limit reached!
% 15.87/3.62 % (12705)------------------------------
% 15.87/3.62 % (12705)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.87/3.62 % (12705)Termination reason: Unknown
% 15.87/3.62 % (12705)Termination phase: Saturation
% 15.87/3.62
% 15.87/3.62 % (12705)Memory used [KB]: 6780
% 15.87/3.62 % (12705)Time elapsed: 0.212 s
% 15.87/3.62 % (12705)Instructions burned: 771 (million)
% 15.87/3.62 % (12705)------------------------------
% 15.87/3.62 % (12705)------------------------------
% 15.87/3.62 % (12699)Instruction limit reached!
% 15.87/3.62 % (12699)------------------------------
% 15.87/3.62 % (12699)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.87/3.62 % (12699)Termination reason: Unknown
% 15.87/3.62 % (12699)Termination phase: Saturation
% 15.87/3.62
% 15.87/3.62 % (12699)Memory used [KB]: 15863
% 15.87/3.62 % (12699)Time elapsed: 0.550 s
% 15.87/3.62 % (12699)Instructions burned: 1827 (million)
% 15.87/3.62 % (12699)------------------------------
% 15.87/3.62 % (12699)------------------------------
% 15.87/3.63 % (12706)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_12319 for (2978ds/794Mi)
% 15.87/3.63 % (12707)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on DTF2THF_12319 for (2978ds/464Mi)
% 15.87/3.65 % (12681)Instruction limit reached!
% 15.87/3.65 % (12681)------------------------------
% 15.87/3.65 % (12681)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.87/3.65 % (12681)Termination reason: Unknown
% 15.87/3.65 % (12681)Termination phase: Saturation
% 15.87/3.65
% 15.87/3.65 % (12681)Memory used [KB]: 9594
% 15.87/3.65 % (12681)Time elapsed: 1.283 s
% 15.87/3.65 % (12681)Instructions burned: 5207 (million)
% 15.87/3.65 % (12681)------------------------------
% 15.87/3.65 % (12681)------------------------------
% 15.87/3.66 % (12708)ott+21_1:3_avsq=on:bd=off:cnfonf=lazy_gen:fe=off:hud=10:ixr=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=1376:si=on:rtra=on_0 on DTF2THF_12319 for (2978ds/1376Mi)
% 16.92/3.76 % (12678)Instruction limit reached!
% 16.92/3.76 % (12678)------------------------------
% 16.92/3.76 % (12678)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.92/3.76 % (12678)Termination reason: Unknown
% 16.92/3.76 % (12678)Termination phase: Saturation
% 16.92/3.76
% 16.92/3.76 % (12678)Memory used [KB]: 14711
% 16.92/3.76 % (12678)Time elapsed: 1.421 s
% 16.92/3.76 % (12678)Instructions burned: 4437 (million)
% 16.92/3.76 % (12678)------------------------------
% 16.92/3.76 % (12678)------------------------------
% 16.92/3.77 % (12707)Instruction limit reached!
% 16.92/3.77 % (12707)------------------------------
% 16.92/3.77 % (12707)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.92/3.77 % (12707)Termination reason: Unknown
% 16.92/3.77 % (12707)Termination phase: Saturation
% 16.92/3.77
% 16.92/3.77 % (12707)Memory used [KB]: 7931
% 16.92/3.77 % (12707)Time elapsed: 0.142 s
% 16.92/3.77 % (12707)Instructions burned: 465 (million)
% 16.92/3.77 % (12707)------------------------------
% 16.92/3.77 % (12707)------------------------------
% 16.92/3.77 % (12709)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on DTF2THF_12319 for (2976ds/906Mi)
% 16.92/3.78 % (12710)lrs+1002_1:16_bd=off:e2e=on:fde=unused:kws=precedence:sac=on:sos=on:ss=axioms:i=434:si=on:rtra=on_0 on DTF2THF_12319 for (2976ds/434Mi)
% 17.24/3.84 % (12683)Instruction limit reached!
% 17.24/3.84 % (12683)------------------------------
% 17.24/3.84 % (12683)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.24/3.84 % (12683)Termination reason: Unknown
% 17.24/3.84 % (12683)Termination phase: Saturation
% 17.24/3.84
% 17.24/3.84 % (12683)Memory used [KB]: 10746
% 17.24/3.84 % (12683)Time elapsed: 1.351 s
% 17.24/3.84 % (12683)Instructions burned: 4350 (million)
% 17.24/3.84 % (12683)------------------------------
% 17.24/3.84 % (12683)------------------------------
% 17.24/3.85 % (12711)lrs+10_5:4_cnfonf=conj_eager:fe=axiom:hflw=5:hfsq=on:hfsqc=10:hfsql=off:hud=10:plsq=on:sgt=5:spb=goal_then_units:ss=axioms:i=865:si=on:rtra=on_0 on DTF2THF_12319 for (2976ds/865Mi)
% 17.24/3.87 % (12706)Instruction limit reached!
% 17.24/3.87 % (12706)------------------------------
% 17.24/3.87 % (12706)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.24/3.87 % (12706)Termination reason: Unknown
% 17.24/3.87 % (12706)Termination phase: Saturation
% 17.24/3.87
% 17.24/3.87 % (12706)Memory used [KB]: 4093
% 17.24/3.87 % (12706)Time elapsed: 0.249 s
% 17.24/3.87 % (12706)Instructions burned: 796 (million)
% 17.24/3.87 % (12706)------------------------------
% 17.24/3.87 % (12706)------------------------------
% 17.24/3.88 % (12712)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=593:si=on:rtra=on_0 on DTF2THF_12319 for (2975ds/593Mi)
% 17.57/3.91 % (12710)Instruction limit reached!
% 17.57/3.91 % (12710)------------------------------
% 17.57/3.91 % (12710)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.57/3.91 % (12710)Termination reason: Unknown
% 17.57/3.91 % (12710)Termination phase: Saturation
% 17.57/3.91
% 17.57/3.91 % (12710)Memory used [KB]: 8827
% 17.57/3.91 % (12710)Time elapsed: 0.131 s
% 17.57/3.91 % (12710)Instructions burned: 434 (million)
% 17.57/3.91 % (12710)------------------------------
% 17.57/3.91 % (12710)------------------------------
% 17.57/3.92 % (12713)dis+10_1:1_sd=2:sgt=20:slsq=on:ss=axioms:st=6.0:i=443:si=on:rtra=on_0 on DTF2THF_12319 for (2975ds/443Mi)
% 17.57/4.00 % (12708)Instruction limit reached!
% 17.57/4.00 % (12708)------------------------------
% 17.57/4.00 % (12708)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.57/4.00 % (12708)Termination reason: Unknown
% 17.57/4.00 % (12708)Termination phase: Saturation
% 17.57/4.00
% 17.57/4.00 % (12708)Memory used [KB]: 8187
% 17.57/4.00 % (12708)Time elapsed: 0.340 s
% 17.57/4.00 % (12708)Instructions burned: 1379 (million)
% 17.57/4.00 % (12708)------------------------------
% 17.57/4.00 % (12708)------------------------------
% 17.57/4.01 % (12714)dis+10_1:1_atotf=0.1:cbe=off:sd=3:ss=axioms:st=2.0:i=594:si=on:rtra=on_0 on DTF2THF_12319 for (2974ds/594Mi)
% 17.57/4.02 % (12712)Instruction limit reached!
% 17.57/4.02 % (12712)------------------------------
% 17.57/4.02 % (12712)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.57/4.02 % (12712)Termination reason: Unknown
% 17.57/4.02 % (12712)Termination phase: Saturation
% 17.57/4.02
% 17.57/4.02 % (12712)Memory used [KB]: 6652
% 17.57/4.02 % (12712)Time elapsed: 0.139 s
% 17.57/4.02 % (12712)Instructions burned: 598 (million)
% 17.57/4.02 % (12712)------------------------------
% 17.57/4.02 % (12712)------------------------------
% 20.33/4.03 % (12715)ott+10_1:1024_anc=none:bd=off:e2e=on:fde=none:fsr=off:hud=10:ixr=off:nm=4:nwc=5.0:spb=goal:i=327:si=on:rtra=on_0 on DTF2THF_12319 for (2974ds/327Mi)
% 20.33/4.05 % (12709)Instruction limit reached!
% 20.33/4.05 % (12709)------------------------------
% 20.33/4.05 % (12709)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.33/4.05 % (12709)Termination reason: Unknown
% 20.33/4.05 % (12709)Termination phase: Saturation
% 20.33/4.05
% 20.33/4.05 % (12709)Memory used [KB]: 9083
% 20.33/4.05 % (12709)Time elapsed: 0.276 s
% 20.33/4.05 % (12709)Instructions burned: 907 (million)
% 20.33/4.05 % (12709)------------------------------
% 20.33/4.05 % (12709)------------------------------
% 20.33/4.06 % (12713)Instruction limit reached!
% 20.33/4.06 % (12713)------------------------------
% 20.33/4.06 % (12713)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.33/4.06 % (12713)Termination reason: Unknown
% 20.33/4.06 % (12713)Termination phase: Saturation
% 20.33/4.06
% 20.33/4.06 % (12713)Memory used [KB]: 7803
% 20.33/4.06 % (12713)Time elapsed: 0.137 s
% 20.33/4.06 % (12713)Instructions burned: 444 (million)
% 20.33/4.06 % (12713)------------------------------
% 20.33/4.06 % (12713)------------------------------
% 20.33/4.06 % (12716)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=5411:si=on:rtra=on_0 on DTF2THF_12319 for (2974ds/5411Mi)
% 20.33/4.07 % (12717)lrs+10_1:20_au=on:c=on:cbe=off:cnfonf=lazy_gen:ins=1:plsq=on:plsqc=1:plsqr=46,31:sac=on:i=1762:si=on:rtra=on_0 on DTF2THF_12319 for (2973ds/1762Mi)
% 20.33/4.12 % (12711)Instruction limit reached!
% 20.33/4.12 % (12711)------------------------------
% 20.33/4.12 % (12711)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.33/4.12 % (12711)Termination reason: Unknown
% 20.33/4.12 % (12711)Termination phase: Saturation
% 20.33/4.12
% 20.33/4.12 % (12711)Memory used [KB]: 8571
% 20.33/4.12 % (12711)Time elapsed: 0.269 s
% 20.33/4.12 % (12711)Instructions burned: 868 (million)
% 20.33/4.12 % (12711)------------------------------
% 20.33/4.12 % (12711)------------------------------
% 20.75/4.13 % (12718)dis+1003_1:64_cha=on:cnfonf=lazy_gen:hud=9:nwc=8.0:prag=on:i=96:si=on:rtra=on_0 on DTF2THF_12319 for (2973ds/96Mi)
% 20.75/4.14 % (12715)Instruction limit reached!
% 20.75/4.14 % (12715)------------------------------
% 20.75/4.14 % (12715)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.75/4.14 % (12715)Termination reason: Unknown
% 20.75/4.14 % (12715)Termination phase: Saturation
% 20.75/4.14
% 20.75/4.14 % (12715)Memory used [KB]: 9338
% 20.75/4.14 % (12715)Time elapsed: 0.106 s
% 20.75/4.14 % (12715)Instructions burned: 327 (million)
% 20.75/4.14 % (12715)------------------------------
% 20.75/4.14 % (12715)------------------------------
% 20.75/4.14 % (12719)lrs+21_1:1_hud=5:kws=inv_frequency:nm=16:nwc=2.0:prag=on:sos=on:ss=axioms:i=503:si=on:rtra=on_0 on DTF2THF_12319 for (2973ds/503Mi)
% 20.75/4.15 % (12718)Instruction limit reached!
% 20.75/4.15 % (12718)------------------------------
% 20.75/4.15 % (12718)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.75/4.15 % (12718)Termination reason: Unknown
% 20.75/4.15 % (12718)Termination phase: Saturation
% 20.75/4.15
% 20.75/4.15 % (12718)Memory used [KB]: 6396
% 20.75/4.15 % (12718)Time elapsed: 0.026 s
% 20.75/4.15 % (12718)Instructions burned: 99 (million)
% 20.75/4.15 % (12718)------------------------------
% 20.75/4.15 % (12718)------------------------------
% 20.75/4.16 % (12720)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on DTF2THF_12319 for (2973ds/90Mi)
% 20.75/4.19 % (12720)Instruction limit reached!
% 20.75/4.19 % (12720)------------------------------
% 20.75/4.19 % (12720)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.75/4.19 % (12720)Termination reason: Unknown
% 20.75/4.19 % (12720)Termination phase: Saturation
% 20.75/4.19
% 20.75/4.19 % (12720)Memory used [KB]: 6908
% 20.75/4.19 % (12720)Time elapsed: 0.026 s
% 20.75/4.19 % (12720)Instructions burned: 91 (million)
% 20.75/4.19 % (12720)------------------------------
% 20.75/4.19 % (12720)------------------------------
% 21.06/4.20 % (12721)lrs+10_1:64_hud=5:plsq=on:plsqr=2011171,524288:i=593:si=on:rtra=on_0 on DTF2THF_12319 for (2972ds/593Mi)
% 21.06/4.20 % (12714)Instruction limit reached!
% 21.06/4.20 % (12714)------------------------------
% 21.06/4.20 % (12714)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.06/4.20 % (12714)Termination reason: Unknown
% 21.06/4.20 % (12714)Termination phase: Saturation
% 21.06/4.20
% 21.06/4.20 % (12714)Memory used [KB]: 7803
% 21.06/4.20 % (12714)Time elapsed: 0.207 s
% 21.06/4.20 % (12714)Instructions burned: 595 (million)
% 21.06/4.20 % (12714)------------------------------
% 21.06/4.20 % (12714)------------------------------
% 21.06/4.21 % (12722)dis-1002_1:1_alpa=false:apa=on:au=on:bd=off:cnfonf=off:e2e=on:er=filter:fde=unused:plsq=on:plsqr=9699663,1048576:s2a=on:sos=on:sp=unary_first:i=1512:si=on:rtra=on_0 on DTF2THF_12319 for (2972ds/1512Mi)
% 21.06/4.27 % (12703)Instruction limit reached!
% 21.06/4.27 % (12703)------------------------------
% 21.06/4.27 % (12703)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.06/4.27 % (12703)Termination reason: Unknown
% 21.06/4.27 % (12703)Termination phase: Saturation
% 21.06/4.27
% 21.06/4.27 % (12703)Memory used [KB]: 7036
% 21.06/4.27 % (12703)Time elapsed: 1.081 s
% 21.06/4.27 % (12703)Instructions burned: 4718 (million)
% 21.06/4.27 % (12703)------------------------------
% 21.06/4.27 % (12703)------------------------------
% 21.06/4.28 % (12723)lrs+1002_1:128_cbe=off:cnfonf=lazy_not_gen_be_off:ins=1:i=569:si=on:rtra=on_0 on DTF2THF_12319 for (2971ds/569Mi)
% 21.44/4.30 % (12719)Instruction limit reached!
% 21.44/4.30 % (12719)------------------------------
% 21.44/4.30 % (12719)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.44/4.30 % (12719)Termination reason: Unknown
% 21.44/4.30 % (12719)Termination phase: Saturation
% 21.44/4.30
% 21.44/4.30 % (12719)Memory used [KB]: 7803
% 21.44/4.30 % (12719)Time elapsed: 0.157 s
% 21.44/4.30 % (12719)Instructions burned: 504 (million)
% 21.44/4.30 % (12719)------------------------------
% 21.44/4.30 % (12719)------------------------------
% 21.44/4.31 % (12724)ott+1002_1:1_bd=off:cnfonf=off:e2e=on:fd=off:fe=axiom:hud=5:prag=on:sos=on:i=501:si=on:rtra=on_0 on DTF2THF_12319 for (2971ds/501Mi)
% 21.44/4.38 % (12721)Instruction limit reached!
% 21.44/4.38 % (12721)------------------------------
% 21.44/4.38 % (12721)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.44/4.38 % (12721)Termination reason: Unknown
% 21.44/4.38 % (12721)Termination phase: Saturation
% 21.44/4.38
% 21.44/4.38 % (12721)Memory used [KB]: 8059
% 21.44/4.38 % (12721)Time elapsed: 0.182 s
% 21.44/4.38 % (12721)Instructions burned: 595 (million)
% 21.44/4.38 % (12721)------------------------------
% 21.44/4.38 % (12721)------------------------------
% 21.44/4.39 % (12725)lrs+1010_1:3_cnfonf=conj_eager:fsr=off:prag=on:sd=4:sgt=10:ss=axioms:i=562:si=on:rtra=on_0 on DTF2THF_12319 for (2970ds/562Mi)
% 21.91/4.42 % (12723)Instruction limit reached!
% 21.91/4.42 % (12723)------------------------------
% 21.91/4.42 % (12723)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.91/4.42 % (12723)Termination reason: Unknown
% 21.91/4.42 % (12723)Termination phase: Saturation
% 21.91/4.42
% 21.91/4.42 % (12723)Memory used [KB]: 8827
% 21.91/4.42 % (12723)Time elapsed: 0.140 s
% 21.91/4.42 % (12723)Instructions burned: 570 (million)
% 21.91/4.42 % (12723)------------------------------
% 21.91/4.42 % (12723)------------------------------
% 21.91/4.42 % (12726)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_12319 for (2970ds/406Mi)
% 21.91/4.47 % (12724)Instruction limit reached!
% 21.91/4.47 % (12724)------------------------------
% 21.91/4.47 % (12724)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.91/4.47 % (12724)Termination reason: Unknown
% 21.91/4.47 % (12724)Termination phase: Saturation
% 21.91/4.47
% 21.91/4.47 % (12724)Memory used [KB]: 8827
% 21.91/4.47 % (12724)Time elapsed: 0.156 s
% 21.91/4.47 % (12724)Instructions burned: 502 (million)
% 21.91/4.47 % (12724)------------------------------
% 21.91/4.47 % (12724)------------------------------
% 21.91/4.48 % (12727)dis+1004_1:128_au=on:cbe=off:e2e=on:sac=on:i=582:si=on:rtra=on_0 on DTF2THF_12319 for (2969ds/582Mi)
% 22.32/4.51 % (12717)Instruction limit reached!
% 22.32/4.51 % (12717)------------------------------
% 22.32/4.51 % (12717)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.32/4.51 % (12717)Termination reason: Unknown
% 22.32/4.51 % (12717)Termination phase: Saturation
% 22.32/4.51
% 22.32/4.51 % (12717)Memory used [KB]: 10874
% 22.32/4.51 % (12717)Time elapsed: 0.439 s
% 22.32/4.51 % (12717)Instructions burned: 1764 (million)
% 22.32/4.51 % (12717)------------------------------
% 22.32/4.51 % (12717)------------------------------
% 22.32/4.52 % (12728)lrs+2_1:1_au=on:bd=off:bsr=unit_only:sd=2:sgt=32:sos=all:ss=axioms:i=456:si=on:rtra=on_0 on DTF2THF_12319 for (2969ds/456Mi)
% 22.32/4.54 % (12725)Instruction limit reached!
% 22.32/4.54 % (12725)------------------------------
% 22.32/4.54 % (12725)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.32/4.54 % (12725)Termination reason: Unknown
% 22.32/4.54 % (12725)Termination phase: Saturation
% 22.32/4.54
% 22.32/4.54 % (12725)Memory used [KB]: 7164
% 22.32/4.54 % (12725)Time elapsed: 0.151 s
% 22.32/4.54 % (12725)Instructions burned: 563 (million)
% 22.32/4.54 % (12725)------------------------------
% 22.32/4.54 % (12725)------------------------------
% 22.32/4.54 % (12726)Instruction limit reached!
% 22.32/4.54 % (12726)------------------------------
% 22.32/4.54 % (12726)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.32/4.54 % (12726)Termination reason: Unknown
% 22.32/4.54 % (12726)Termination phase: Saturation
% 22.32/4.54
% 22.32/4.54 % (12726)Memory used [KB]: 7291
% 22.32/4.54 % (12726)Time elapsed: 0.121 s
% 22.32/4.54 % (12726)Instructions burned: 408 (million)
% 22.32/4.54 % (12726)------------------------------
% 22.32/4.54 % (12726)------------------------------
% 22.32/4.55 % (12729)lrs+1010_1:1_au=on:cbe=off:cnfonf=conj_eager:tgt=ground:i=393:si=on:rtra=on_0 on DTF2THF_12319 for (2969ds/393Mi)
% 22.32/4.55 % (12730)lrs+1010_1:6_au=on:cnfonf=conj_eager:nwc=10.0:pe=on:prag=on:s2a=on:ss=axioms:st=1.5:i=1335:si=on:rtra=on_0 on DTF2THF_12319 for (2969ds/1335Mi)
% 23.16/4.65 % (12728)Instruction limit reached!
% 23.16/4.65 % (12728)------------------------------
% 23.16/4.65 % (12728)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.16/4.65 % (12728)Termination reason: Unknown
% 23.16/4.65 % (12728)Termination phase: Saturation
% 23.16/4.65
% 23.16/4.65 % (12728)Memory used [KB]: 7803
% 23.16/4.65 % (12728)Time elapsed: 0.137 s
% 23.16/4.65 % (12728)Instructions burned: 457 (million)
% 23.16/4.65 % (12728)------------------------------
% 23.16/4.65 % (12728)------------------------------
% 23.16/4.66 % (12727)Instruction limit reached!
% 23.16/4.66 % (12727)------------------------------
% 23.16/4.66 % (12727)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.16/4.66 % (12727)Termination reason: Unknown
% 23.16/4.66 % (12727)Termination phase: Saturation
% 23.16/4.66
% 23.16/4.66 % (12727)Memory used [KB]: 8955
% 23.16/4.66 % (12727)Time elapsed: 0.184 s
% 23.16/4.66 % (12727)Instructions burned: 582 (million)
% 23.16/4.66 % (12727)------------------------------
% 23.16/4.66 % (12727)------------------------------
% 23.16/4.66 % (12731)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=3373:si=on:rtra=on_0 on DTF2THF_12319 for (2968ds/3373Mi)
% 23.16/4.66 % (12729)Instruction limit reached!
% 23.16/4.66 % (12729)------------------------------
% 23.16/4.66 % (12729)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.16/4.66 % (12729)Termination reason: Unknown
% 23.16/4.66 % (12729)Termination phase: Saturation
% 23.16/4.66
% 23.16/4.66 % (12729)Memory used [KB]: 8187
% 23.16/4.66 % (12729)Time elapsed: 0.117 s
% 23.16/4.66 % (12729)Instructions burned: 394 (million)
% 23.16/4.66 % (12729)------------------------------
% 23.16/4.66 % (12729)------------------------------
% 23.16/4.67 % (12732)dis+10_1:1024_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=32,1:spb=goal_then_units:i=474:si=on:rtra=on_0 on DTF2THF_12319 for (2968ds/474Mi)
% 23.16/4.67 % (12733)lrs+1002_1:16_amm=sco:cnfonf=lazy_pi_sigma_gen:fe=off:nm=60:piset=all_but_not_eq:plsq=on:plsqc=1:plsqr=2,1:rawr=on:sp=occurrence:ss=included:st=-1.0:i=157:si=on:rtra=on_0 on DTF2THF_12319 for (2967ds/157Mi)
% 23.16/4.68 % (12722)Instruction limit reached!
% 23.16/4.68 % (12722)------------------------------
% 23.16/4.68 % (12722)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.16/4.68 % (12722)Termination reason: Unknown
% 23.16/4.68 % (12722)Termination phase: Saturation
% 23.16/4.68
% 23.16/4.68 % (12722)Memory used [KB]: 10490
% 23.16/4.68 % (12722)Time elapsed: 0.474 s
% 23.16/4.68 % (12722)Instructions burned: 1512 (million)
% 23.16/4.68 % (12722)------------------------------
% 23.16/4.68 % (12722)------------------------------
% 23.16/4.69 % (12734)dis+1010_1:1_amm=off:cs=on:kws=precedence:nwc=10.0:piset=all:s2a=on:sac=on:sp=unary_frequency:spb=goal:ss=axioms:st=3.0:i=590:si=on:rtra=on_0 on DTF2THF_12319 for (2967ds/590Mi)
% 24.20/4.71 % (12733)Instruction limit reached!
% 24.20/4.71 % (12733)------------------------------
% 24.20/4.71 % (12733)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.20/4.71 % (12733)Termination reason: Unknown
% 24.20/4.71 % (12733)Termination phase: Saturation
% 24.20/4.71
% 24.20/4.71 % (12733)Memory used [KB]: 6524
% 24.20/4.71 % (12733)Time elapsed: 0.040 s
% 24.20/4.71 % (12733)Instructions burned: 157 (million)
% 24.20/4.71 % (12733)------------------------------
% 24.20/4.71 % (12733)------------------------------
% 24.20/4.72 % (12735)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=104:si=on:rtra=on_0 on DTF2THF_12319 for (2967ds/104Mi)
% 24.20/4.75 % (12735)Instruction limit reached!
% 24.20/4.75 % (12735)------------------------------
% 24.20/4.75 % (12735)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.20/4.75 % (12735)Termination reason: Unknown
% 24.20/4.75 % (12735)Termination phase: Saturation
% 24.20/4.75
% 24.20/4.75 % (12735)Memory used [KB]: 6780
% 24.20/4.75 % (12735)Time elapsed: 0.029 s
% 24.20/4.75 % (12735)Instructions burned: 106 (million)
% 24.20/4.75 % (12735)------------------------------
% 24.20/4.75 % (12735)------------------------------
% 24.20/4.76 % (12736)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=414:si=on:rtra=on_0 on DTF2THF_12319 for (2967ds/414Mi)
% 24.20/4.78 % (12732)Instruction limit reached!
% 24.20/4.78 % (12732)------------------------------
% 24.20/4.78 % (12732)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.20/4.78 % (12732)Termination reason: Unknown
% 24.20/4.78 % (12732)Termination phase: Saturation
% 24.20/4.78
% 24.20/4.78 % (12732)Memory used [KB]: 9083
% 24.20/4.78 % (12732)Time elapsed: 0.115 s
% 24.20/4.78 % (12732)Instructions burned: 475 (million)
% 24.20/4.78 % (12732)------------------------------
% 24.20/4.78 % (12732)------------------------------
% 24.20/4.79 % (12737)dis+10_1:1_av=off:bsd=on:bsr=unit_only:fd=off:hud=8:nm=16:prag=on:i=715:si=on:rtra=on_0 on DTF2THF_12319 for (2966ds/715Mi)
% 24.51/4.86 % (12736)Instruction limit reached!
% 24.51/4.86 % (12736)------------------------------
% 24.51/4.86 % (12736)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.51/4.86 % (12736)Termination reason: Unknown
% 24.51/4.86 % (12736)Termination phase: Saturation
% 24.51/4.86
% 24.51/4.86 % (12736)Memory used [KB]: 6524
% 24.51/4.86 % (12736)Time elapsed: 0.099 s
% 24.51/4.86 % (12736)Instructions burned: 417 (million)
% 24.51/4.86 % (12736)------------------------------
% 24.51/4.86 % (12736)------------------------------
% 24.51/4.86 % (12734)Instruction limit reached!
% 24.51/4.86 % (12734)------------------------------
% 24.51/4.86 % (12734)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.51/4.86 % (12734)Termination reason: Unknown
% 24.51/4.86 % (12734)Termination phase: Saturation
% 24.51/4.86
% 24.51/4.86 % (12734)Memory used [KB]: 7675
% 24.51/4.86 % (12734)Time elapsed: 0.171 s
% 24.51/4.86 % (12734)Instructions burned: 592 (million)
% 24.51/4.86 % (12734)------------------------------
% 24.51/4.86 % (12734)------------------------------
% 24.51/4.87 % (12738)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=961:si=on:rtra=on_0 on DTF2THF_12319 for (2966ds/961Mi)
% 24.51/4.87 % (12739)lrs-1002_1:128_abs=on:bd=preordered:cbe=off:e2e=on:fde=unused:fe=off:tgt=full:i=1213:si=on:rtra=on_0 on DTF2THF_12319 for (2966ds/1213Mi)
% 24.89/4.92 % (12730)Instruction limit reached!
% 24.89/4.92 % (12730)------------------------------
% 24.89/4.92 % (12730)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.89/4.92 % (12730)Termination reason: Unknown
% 24.89/4.92 % (12730)Termination phase: Saturation
% 24.89/4.92
% 24.89/4.92 % (12730)Memory used [KB]: 7803
% 24.89/4.92 % (12730)Time elapsed: 0.366 s
% 24.89/4.92 % (12730)Instructions burned: 1335 (million)
% 24.89/4.92 % (12730)------------------------------
% 24.89/4.92 % (12730)------------------------------
% 24.89/4.93 % (12740)lrs+1002_1:12_bd=off:hud=1:ntd=on:piset=equals:prag=on:i=1979:si=on:rtra=on_0 on DTF2THF_12319 for (2965ds/1979Mi)
% 24.89/5.01 % (12737)Instruction limit reached!
% 24.89/5.01 % (12737)------------------------------
% 24.89/5.01 % (12737)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.89/5.01 % (12737)Termination reason: Unknown
% 24.89/5.01 % (12737)Termination phase: Saturation
% 24.89/5.01
% 24.89/5.01 % (12737)Memory used [KB]: 3582
% 24.89/5.01 % (12737)Time elapsed: 0.222 s
% 24.89/5.01 % (12737)Instructions burned: 715 (million)
% 24.89/5.01 % (12737)------------------------------
% 24.89/5.01 % (12737)------------------------------
% 24.89/5.02 % (12741)dis+1002_1:1_amm=off:au=on:bsd=on:cbe=off:cnfonf=lazy_gen:sp=unary_frequency:i=481:si=on:rtra=on_0 on DTF2THF_12319 for (2964ds/481Mi)
% 27.98/5.14 % (12741)Instruction limit reached!
% 27.98/5.14 % (12741)------------------------------
% 27.98/5.14 % (12741)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.98/5.14 % (12741)Termination reason: Unknown
% 27.98/5.14 % (12741)Termination phase: Saturation
% 27.98/5.14
% 27.98/5.14 % (12741)Memory used [KB]: 9083
% 27.98/5.14 % (12741)Time elapsed: 0.120 s
% 27.98/5.14 % (12741)Instructions burned: 481 (million)
% 27.98/5.14 % (12741)------------------------------
% 27.98/5.14 % (12741)------------------------------
% 27.98/5.15 % (12742)dis+10_8:1_apa=on:cnfonf=off:e2e=on:plsq=on:plsqc=1:plsqr=32,1:ss=axioms:i=783:si=on:rtra=on_0 on DTF2THF_12319 for (2963ds/783Mi)
% 27.98/5.17 % (12738)Instruction limit reached!
% 27.98/5.17 % (12738)------------------------------
% 27.98/5.17 % (12738)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.98/5.17 % (12738)Termination reason: Unknown
% 27.98/5.17 % (12738)Termination phase: Saturation
% 27.98/5.17
% 27.98/5.17 % (12738)Memory used [KB]: 8187
% 27.98/5.17 % (12738)Time elapsed: 0.301 s
% 27.98/5.17 % (12738)Instructions burned: 963 (million)
% 27.98/5.17 % (12738)------------------------------
% 27.98/5.17 % (12738)------------------------------
% 27.98/5.18 % (12743)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=432:si=on:rtra=on_0 on DTF2THF_12319 for (2962ds/432Mi)
% 28.53/5.25 % (12739)Instruction limit reached!
% 28.53/5.25 % (12739)------------------------------
% 28.53/5.25 % (12739)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.53/5.25 % (12739)Termination reason: Unknown
% 28.53/5.25 % (12739)Termination phase: Saturation
% 28.53/5.25
% 28.53/5.25 % (12739)Memory used [KB]: 11257
% 28.53/5.25 % (12739)Time elapsed: 0.383 s
% 28.53/5.25 % (12739)Instructions burned: 1215 (million)
% 28.53/5.25 % (12739)------------------------------
% 28.53/5.25 % (12739)------------------------------
% 28.53/5.26 % (12744)lrs+1010_1:1_atotf=0.5:au=on:cbe=off:cnfonf=lazy_not_be_gen:fe=off:nwc=5.0:spb=units:i=1670:si=on:rtra=on_0 on DTF2THF_12319 for (2962ds/1670Mi)
% 28.99/5.31 % (12743)Instruction limit reached!
% 28.99/5.31 % (12743)------------------------------
% 28.99/5.31 % (12743)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.99/5.31 % (12743)Termination reason: Unknown
% 28.99/5.31 % (12743)Termination phase: Saturation
% 28.99/5.31
% 28.99/5.31 % (12743)Memory used [KB]: 7803
% 28.99/5.31 % (12743)Time elapsed: 0.131 s
% 28.99/5.31 % (12743)Instructions burned: 434 (million)
% 28.99/5.31 % (12743)------------------------------
% 28.99/5.31 % (12743)------------------------------
% 28.99/5.32 % (12745)dis+2_1:1_au=on:hfaw=0:hfsq=on:sp=weighted_frequency:i=90:si=on:rtra=on_0 on DTF2THF_12319 for (2961ds/90Mi)
% 28.99/5.34 % (12745)Instruction limit reached!
% 28.99/5.34 % (12745)------------------------------
% 28.99/5.34 % (12745)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.99/5.34 % (12745)Termination reason: Unknown
% 28.99/5.34 % (12745)Termination phase: Saturation
% 28.99/5.34
% 28.99/5.34 % (12745)Memory used [KB]: 6524
% 28.99/5.34 % (12745)Time elapsed: 0.025 s
% 28.99/5.34 % (12745)Instructions burned: 91 (million)
% 28.99/5.34 % (12745)------------------------------
% 28.99/5.34 % (12745)------------------------------
% 28.99/5.35 % (12746)dis+10_1:1_au=on:cnfonf=lazy_gen:ixr=off:plsq=on:plsqc=1:plsqr=32,1:i=346:si=on:rtra=on_0 on DTF2THF_12319 for (2961ds/346Mi)
% 28.99/5.40 % (12742)Instruction limit reached!
% 28.99/5.40 % (12742)------------------------------
% 28.99/5.40 % (12742)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.99/5.40 % (12742)Termination reason: Unknown
% 28.99/5.40 % (12742)Termination phase: Saturation
% 28.99/5.40
% 28.99/5.40 % (12742)Memory used [KB]: 9850
% 28.99/5.40 % (12742)Time elapsed: 0.246 s
% 28.99/5.40 % (12742)Instructions burned: 783 (million)
% 28.99/5.40 % (12742)------------------------------
% 28.99/5.40 % (12742)------------------------------
% 29.82/5.41 % (12747)dis+1002_1:1_cnfonf=lazy_not_gen:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=401:si=on:rtra=on_0 on DTF2THF_12319 for (2960ds/401Mi)
% 29.82/5.43 % (12746)Instruction limit reached!
% 29.82/5.43 % (12746)------------------------------
% 29.82/5.43 % (12746)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.82/5.43 % (12746)Termination reason: Unknown
% 29.82/5.43 % (12746)Termination phase: Saturation
% 29.82/5.43
% 29.82/5.43 % (12746)Memory used [KB]: 8955
% 29.82/5.43 % (12746)Time elapsed: 0.085 s
% 29.82/5.43 % (12746)Instructions burned: 346 (million)
% 29.82/5.43 % (12746)------------------------------
% 29.82/5.43 % (12746)------------------------------
% 29.82/5.44 % (12748)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=6454:si=on:rtra=on_0 on DTF2THF_12319 for (2960ds/6454Mi)
% 30.31/5.50 % (12747)Instruction limit reached!
% 30.31/5.50 % (12747)------------------------------
% 30.31/5.50 % (12747)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.31/5.50 % (12747)Termination reason: Unknown
% 30.31/5.50 % (12747)Termination phase: Saturation
% 30.31/5.50
% 30.31/5.50 % (12747)Memory used [KB]: 6524
% 30.31/5.50 % (12747)Time elapsed: 0.096 s
% 30.31/5.50 % (12747)Instructions burned: 402 (million)
% 30.31/5.50 % (12747)------------------------------
% 30.31/5.50 % (12747)------------------------------
% 30.31/5.51 % (12749)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:kws=arity:prag=on:i=283:si=on:rtra=on_0 on DTF2THF_12319 for (2959ds/283Mi)
% 30.31/5.53 % (12740)Refutation not found, non-redundant clauses discarded% (12740)------------------------------
% 30.31/5.53 % (12740)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.31/5.53 % (12740)Termination reason: Refutation not found, non-redundant clauses discarded
% 30.31/5.53
% 30.31/5.53 % (12740)Memory used [KB]: 8443
% 30.31/5.53 % (12740)Time elapsed: 0.606 s
% 30.31/5.53 % (12740)Instructions burned: 1925 (million)
% 30.31/5.53 % (12740)------------------------------
% 30.31/5.53 % (12740)------------------------------
% 30.31/5.54 % (12750)ott+10_1:1_aac=none:apa=on:au=on:cnfonf=off:ntd=on:nwc=12.0:sos=on:i=865:si=on:rtra=on_0 on DTF2THF_12319 for (2959ds/865Mi)
% 30.77/5.60 % (12749)Instruction limit reached!
% 30.77/5.60 % (12749)------------------------------
% 30.77/5.60 % (12749)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.77/5.60 % (12749)Termination reason: Unknown
% 30.77/5.60 % (12749)Termination phase: Saturation
% 30.77/5.60
% 30.77/5.60 % (12749)Memory used [KB]: 7419
% 30.77/5.60 % (12749)Time elapsed: 0.089 s
% 30.77/5.60 % (12749)Instructions burned: 284 (million)
% 30.77/5.60 % (12749)------------------------------
% 30.77/5.60 % (12749)------------------------------
% 30.77/5.61 % (12751)lrs+1002_3:4_au=on:av=off:cnfonf=off:fd=off:fsr=off:ins=2:sd=1:sos=on:ss=axioms:i=4528:si=on:rtra=on_0 on DTF2THF_12319 for (2958ds/4528Mi)
% 30.77/5.66 % (12751)Refutation not found, incomplete strategy
% 30.77/5.66 % (12751)------------------------------
% 30.77/5.66 % (12751)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.77/5.66 % (12751)Termination reason: Refutation not found, incomplete strategy
% 30.77/5.66
% 30.77/5.66
% 30.77/5.66 % (12751)Memory used [KB]: 2046
% 30.77/5.66 % (12751)Time elapsed: 0.055 s
% 30.77/5.66 % (12751)Instructions burned: 206 (million)
% 30.77/5.66 % (12751)------------------------------
% 30.77/5.66 % (12751)------------------------------
% 30.77/5.67 % (12752)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=1001:si=on:rtra=on_0 on DTF2THF_12319 for (2957ds/1001Mi)
% 30.77/5.67 % (12744)Instruction limit reached!
% 30.77/5.67 % (12744)------------------------------
% 30.77/5.67 % (12744)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.77/5.67 % (12744)Termination reason: Unknown
% 30.77/5.67 % (12744)Termination phase: Saturation
% 30.77/5.67
% 30.77/5.67 % (12744)Memory used [KB]: 9594
% 30.77/5.67 % (12744)Time elapsed: 0.410 s
% 30.77/5.67 % (12744)Instructions burned: 1670 (million)
% 30.77/5.67 % (12744)------------------------------
% 30.77/5.67 % (12744)------------------------------
% 30.77/5.68 % (12753)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=102:si=on:rtra=on_0 on DTF2THF_12319 for (2957ds/102Mi)
% 31.65/5.71 % (12753)Instruction limit reached!
% 31.65/5.71 % (12753)------------------------------
% 31.65/5.71 % (12753)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.65/5.71 % (12753)Termination reason: Unknown
% 31.65/5.71 % (12753)Termination phase: Saturation
% 31.65/5.71
% 31.65/5.71 % (12753)Memory used [KB]: 6524
% 31.65/5.71 % (12753)Time elapsed: 0.028 s
% 31.65/5.71 % (12753)Instructions burned: 103 (million)
% 31.65/5.71 % (12753)------------------------------
% 31.65/5.71 % (12753)------------------------------
% 31.65/5.72 % (12754)ott+1010_3:1_nm=20:s2a=on:s2at=3.0:sp=const_frequency:i=952:si=on:rtra=on_0 on DTF2THF_12319 for (2957ds/952Mi)
% 31.65/5.72 % (12731)Instruction limit reached!
% 31.65/5.72 % (12731)------------------------------
% 31.65/5.72 % (12731)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.65/5.72 % (12731)Termination reason: Unknown
% 31.65/5.72 % (12731)Termination phase: Saturation
% 31.65/5.72
% 31.65/5.72 % (12731)Memory used [KB]: 11257
% 31.65/5.72 % (12731)Time elapsed: 1.059 s
% 31.65/5.72 % (12731)Instructions burned: 3375 (million)
% 31.65/5.72 % (12731)------------------------------
% 31.65/5.72 % (12731)------------------------------
% 31.65/5.73 % (12755)lrs+1010_1:1024_add=large:c=on:cbe=off:cnfonf=lazy_gen:fde=none:nm=30:piset=and:sac=on:uhcvi=on:i=578:si=on:rtra=on_0 on DTF2THF_12319 for (2957ds/578Mi)
% 31.65/5.78 % (12716)Refutation not found, non-redundant clauses discarded% (12716)------------------------------
% 31.65/5.78 % (12716)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.65/5.78 % (12716)Termination reason: Refutation not found, non-redundant clauses discarded
% 31.65/5.78
% 31.65/5.78 % (12716)Memory used [KB]: 14967
% 31.65/5.78 % (12716)Time elapsed: 1.719 s
% 31.65/5.78 % (12716)Instructions burned: 5401 (million)
% 31.65/5.78 % (12716)------------------------------
% 31.65/5.78 % (12716)------------------------------
% 31.65/5.79 % (12756)dis+1010_1:4_avsq=on:avsqr=16,1:bet=on:cbe=off:cnfonf=lazy_not_be_gen:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=643:si=on:rtra=on_0 on DTF2THF_12319 for (2956ds/643Mi)
% 31.91/5.80 % (12750)Instruction limit reached!
% 31.91/5.80 % (12750)------------------------------
% 31.91/5.80 % (12750)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.91/5.80 % (12750)Termination reason: Unknown
% 31.91/5.80 % (12750)Termination phase: Saturation
% 31.91/5.80
% 31.91/5.80 % (12750)Memory used [KB]: 7931
% 31.91/5.80 % (12750)Time elapsed: 0.260 s
% 31.91/5.80 % (12750)Instructions burned: 866 (million)
% 31.91/5.80 % (12750)------------------------------
% 31.91/5.80 % (12750)------------------------------
% 31.91/5.81 % (12757)lrs+1010_1:1_cnfonf=off:ntd=on:nwc=3.0:s2a=on:sp=const_frequency:i=865:si=on:rtra=on_0 on DTF2THF_12319 for (2956ds/865Mi)
% 31.91/5.87 % (12755)Instruction limit reached!
% 31.91/5.87 % (12755)------------------------------
% 31.91/5.87 % (12755)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.91/5.87 % (12755)Termination reason: Unknown
% 31.91/5.87 % (12755)Termination phase: Saturation
% 31.91/5.87
% 31.91/5.87 % (12755)Memory used [KB]: 8187
% 31.91/5.87 % (12755)Time elapsed: 0.137 s
% 31.91/5.87 % (12755)Instructions burned: 579 (million)
% 31.91/5.87 % (12755)------------------------------
% 31.91/5.87 % (12755)------------------------------
% 31.91/5.87 % (12758)lrs+10_1:1_au=on:erd=off:s2a=on:s2at=3.0:sos=all:i=1174:si=on:rtra=on_0 on DTF2THF_12319 for (2955ds/1174Mi)
% 32.43/5.90 % (12752)Instruction limit reached!
% 32.43/5.90 % (12752)------------------------------
% 32.43/5.90 % (12752)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.43/5.90 % (12752)Termination reason: Unknown
% 32.43/5.90 % (12752)Termination phase: Saturation
% 32.43/5.90
% 32.43/5.90 % (12752)Memory used [KB]: 7419
% 32.43/5.90 % (12752)Time elapsed: 0.229 s
% 32.43/5.90 % (12752)Instructions burned: 1005 (million)
% 32.43/5.90 % (12752)------------------------------
% 32.43/5.90 % (12752)------------------------------
% 32.43/5.91 % (12759)ott+1010_1:32_apa=on:atotf=0.3:au=on:c=on:cnfonf=off:fe=off:fsr=off:nm=6:piset=or:sac=on:sos=on:i=644:si=on:rtra=on_0 on DTF2THF_12319 for (2955ds/644Mi)
% 32.43/5.91 % (12704)Instruction limit reached!
% 32.43/5.91 % (12704)------------------------------
% 32.43/5.91 % (12704)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.43/5.91 % (12704)Termination reason: Unknown
% 32.43/5.91 % (12704)Termination phase: Saturation
% 32.43/5.91
% 32.43/5.91 % (12704)Memory used [KB]: 22899
% 32.43/5.91 % (12704)Time elapsed: 2.675 s
% 32.43/5.91 % (12704)Instructions burned: 8252 (million)
% 32.43/5.91 % (12704)------------------------------
% 32.43/5.91 % (12704)------------------------------
% 32.43/5.92 % (12760)lrs+10_1:1_alpa=true:au=on:cs=on:tgt=ground:i=1201:si=on:rtra=on_0 on DTF2THF_12319 for (2955ds/1201Mi)
% 32.43/5.94 % (12756)Instruction limit reached!
% 32.43/5.94 % (12756)------------------------------
% 32.43/5.94 % (12756)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.43/5.94 % (12756)Termination reason: Unknown
% 32.43/5.94 % (12756)Termination phase: Saturation
% 32.43/5.94
% 32.43/5.94 % (12756)Memory used [KB]: 8827
% 32.43/5.94 % (12756)Time elapsed: 0.158 s
% 32.43/5.94 % (12756)Instructions burned: 647 (million)
% 32.43/5.94 % (12756)------------------------------
% 32.43/5.94 % (12756)------------------------------
% 32.43/5.95 % (12761)lrs+1666_1:64_cnfonf=lazy_simp:hud=5:plsq=on:plsql=on:plsqr=152565,524288:tnu=2:i=1046:si=on:rtra=on_0 on DTF2THF_12319 for (2955ds/1046Mi)
% 32.43/6.02 % (12754)Instruction limit reached!
% 32.43/6.02 % (12754)------------------------------
% 32.43/6.02 % (12754)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.43/6.02 % (12754)Termination reason: Unknown
% 32.43/6.02 % (12754)Termination phase: Saturation
% 32.43/6.02
% 32.43/6.02 % (12754)Memory used [KB]: 8571
% 32.43/6.02 % (12754)Time elapsed: 0.303 s
% 32.43/6.02 % (12754)Instructions burned: 953 (million)
% 32.43/6.02 % (12754)------------------------------
% 32.43/6.02 % (12754)------------------------------
% 34.08/6.03 % (12762)lrs+1010_1:1_c=on:cnfonf=lazy_simp:fsr=off:hud=5:kws=arity:nm=32:plsq=on:plsqc=1:plsqr=642,29:prag=on:i=222:si=on:rtra=on_0 on DTF2THF_12319 for (2954ds/222Mi)
% 34.08/6.05 % (12757)Instruction limit reached!
% 34.08/6.05 % (12757)------------------------------
% 34.08/6.05 % (12757)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.08/6.05 % (12757)Termination reason: Unknown
% 34.08/6.05 % (12757)Termination phase: Saturation
% 34.08/6.05
% 34.08/6.05 % (12757)Memory used [KB]: 6780
% 34.08/6.05 % (12757)Time elapsed: 0.240 s
% 34.08/6.05 % (12757)Instructions burned: 866 (million)
% 34.08/6.05 % (12757)------------------------------
% 34.08/6.05 % (12757)------------------------------
% 34.08/6.06 % (12763)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=68:si=on:rtra=on_0 on DTF2THF_12319 for (2953ds/68Mi)
% 34.08/6.08 % (12763)Instruction limit reached!
% 34.08/6.08 % (12763)------------------------------
% 34.08/6.08 % (12763)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.08/6.08 % (12763)Termination reason: Unknown
% 34.08/6.08 % (12763)Termination phase: Property scanning
% 34.08/6.08
% 34.08/6.08 % (12763)Memory used [KB]: 1918
% 34.08/6.08 % (12763)Time elapsed: 0.019 s
% 34.08/6.08 % (12763)Instructions burned: 70 (million)
% 34.08/6.08 % (12763)------------------------------
% 34.08/6.08 % (12763)------------------------------
% 34.08/6.08 % (12762)Instruction limit reached!
% 34.08/6.08 % (12762)------------------------------
% 34.08/6.08 % (12762)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.08/6.08 % (12762)Termination reason: Unknown
% 34.08/6.08 % (12762)Termination phase: Saturation
% 34.08/6.08
% 34.08/6.08 % (12762)Memory used [KB]: 6524
% 34.08/6.08 % (12762)Time elapsed: 0.056 s
% 34.08/6.08 % (12762)Instructions burned: 223 (million)
% 34.08/6.08 % (12762)------------------------------
% 34.08/6.08 % (12762)------------------------------
% 34.08/6.09 % (12764)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=454:si=on:rtra=on_0 on DTF2THF_12319 for (2953ds/454Mi)
% 34.08/6.09 % (12765)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=360:si=on:rtra=on_0 on DTF2THF_12319 for (2953ds/360Mi)
% 34.08/6.11 % (12759)Instruction limit reached!
% 34.08/6.11 % (12759)------------------------------
% 34.08/6.11 % (12759)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.08/6.11 % (12759)Termination reason: Unknown
% 34.08/6.11 % (12759)Termination phase: Saturation
% 34.08/6.11
% 34.08/6.11 % (12759)Memory used [KB]: 7036
% 34.08/6.11 % (12759)Time elapsed: 0.197 s
% 34.08/6.11 % (12759)Instructions burned: 644 (million)
% 34.08/6.11 % (12759)------------------------------
% 34.08/6.11 % (12759)------------------------------
% 34.08/6.11 % (12766)lrs+1002_1:16_amm=sco:cnfonf=lazy_pi_sigma_gen:fe=off:nm=60:piset=all_but_not_eq:plsq=on:plsqc=1:plsqr=2,1:rawr=on:sp=occurrence:ss=included:st=-1.0:i=157:si=on:rtra=on_0 on DTF2THF_12319 for (2953ds/157Mi)
% 35.02/6.15 % (12766)Instruction limit reached!
% 35.02/6.15 % (12766)------------------------------
% 35.02/6.15 % (12766)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.02/6.15 % (12766)Termination reason: Unknown
% 35.02/6.15 % (12766)Termination phase: Saturation
% 35.02/6.15
% 35.02/6.15 % (12766)Memory used [KB]: 6524
% 35.02/6.15 % (12766)Time elapsed: 0.040 s
% 35.02/6.15 % (12766)Instructions burned: 157 (million)
% 35.02/6.15 % (12766)------------------------------
% 35.02/6.15 % (12766)------------------------------
% 35.02/6.16 % (12767)ott+1004_1:24_anc=none:cbe=off:cnfonf=lazy_not_gen:fe=off:piset=not:prag=on:rp=on:i=5061:si=on:rtra=on_0 on DTF2THF_12319 for (2952ds/5061Mi)
% 35.02/6.18 % (12765)Instruction limit reached!
% 35.02/6.18 % (12765)------------------------------
% 35.02/6.18 % (12765)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.02/6.18 % (12765)Termination reason: Unknown
% 35.02/6.18 % (12765)Termination phase: Saturation
% 35.02/6.18
% 35.02/6.18 % (12765)Memory used [KB]: 6524
% 35.02/6.18 % (12765)Time elapsed: 0.087 s
% 35.02/6.18 % (12765)Instructions burned: 363 (million)
% 35.02/6.18 % (12765)------------------------------
% 35.02/6.18 % (12765)------------------------------
% 35.02/6.19 % (12768)lrs+1002_1:8_av=off:fd=off:hud=5:tnu=1:i=2401:si=on:rtra=on_0 on DTF2THF_12319 for (2952ds/2401Mi)
% 35.48/6.20 % (12764)Instruction limit reached!
% 35.48/6.20 % (12764)------------------------------
% 35.48/6.20 % (12764)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.48/6.20 % (12764)Termination reason: Unknown
% 35.48/6.20 % (12764)Termination phase: Saturation
% 35.48/6.20
% 35.48/6.20 % (12764)Memory used [KB]: 13432
% 35.48/6.20 % (12764)Time elapsed: 0.113 s
% 35.48/6.20 % (12764)Instructions burned: 457 (million)
% 35.48/6.20 % (12764)------------------------------
% 35.48/6.20 % (12764)------------------------------
% 35.48/6.21 % (12761)Instruction limit reached!
% 35.48/6.21 % (12761)------------------------------
% 35.48/6.21 % (12761)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.48/6.21 % (12761)Termination reason: Unknown
% 35.48/6.21 % (12761)Termination phase: Saturation
% 35.48/6.21
% 35.48/6.21 % (12761)Memory used [KB]: 6652
% 35.48/6.21 % (12761)Time elapsed: 0.253 s
% 35.48/6.21 % (12761)Instructions burned: 1048 (million)
% 35.48/6.21 % (12761)------------------------------
% 35.48/6.21 % (12761)------------------------------
% 35.48/6.21 % (12769)dis+10_1:1_av=off:e2e=on:nm=4:s2a=on:i=5798:si=on:rtra=on_0 on DTF2THF_12319 for (2952ds/5798Mi)
% 35.48/6.22 % (12770)dis+10_1:1_au=on:cnfonf=lazy_gen:ixr=off:plsq=on:plsqc=1:plsqr=32,1:i=346:si=on:rtra=on_0 on DTF2THF_12319 for (2952ds/346Mi)
% 35.48/6.24 % (12758)Instruction limit reached!
% 35.48/6.24 % (12758)------------------------------
% 35.48/6.24 % (12758)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.48/6.24 % (12758)Termination reason: Unknown
% 35.48/6.24 % (12758)Termination phase: Saturation
% 35.48/6.24
% 35.48/6.24 % (12758)Memory used [KB]: 8315
% 35.48/6.24 % (12758)Time elapsed: 0.366 s
% 35.48/6.24 % (12758)Instructions burned: 1176 (million)
% 35.48/6.24 % (12758)------------------------------
% 35.48/6.24 % (12758)------------------------------
% 35.48/6.25 % (12771)lrs+1002_1:1_av=off:bd=off:bet=on:e2e=on:fde=unused:fe=off:plsq=on:prag=on:sos=on:i=1321:si=on:rtra=on_0 on DTF2THF_12319 for (2952ds/1321Mi)
% 35.48/6.28 % (12760)Instruction limit reached!
% 35.48/6.28 % (12760)------------------------------
% 35.48/6.28 % (12760)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.48/6.28 % (12760)Termination reason: Unknown
% 35.48/6.28 % (12760)Termination phase: Saturation
% 35.48/6.28
% 35.48/6.28 % (12760)Memory used [KB]: 9338
% 35.48/6.28 % (12760)Time elapsed: 0.363 s
% 35.48/6.28 % (12760)Instructions burned: 1203 (million)
% 35.48/6.28 % (12760)------------------------------
% 35.48/6.28 % (12760)------------------------------
% 35.48/6.29 % (12772)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:i=1312:si=on:rtra=on_0 on DTF2THF_12319 for (2951ds/1312Mi)
% 35.85/6.30 % (12770)Instruction limit reached!
% 35.85/6.30 % (12770)------------------------------
% 35.85/6.30 % (12770)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.85/6.30 % (12770)Termination reason: Unknown
% 35.85/6.30 % (12770)Termination phase: Saturation
% 35.85/6.30
% 35.85/6.30 % (12770)Memory used [KB]: 8955
% 35.85/6.30 % (12770)Time elapsed: 0.085 s
% 35.85/6.30 % (12770)Instructions burned: 347 (million)
% 35.85/6.30 % (12770)------------------------------
% 35.85/6.30 % (12770)------------------------------
% 35.85/6.31 % (12773)ott+2_8:1_add=large:c=on:cnfonf=off:e2e=on:er=filter:hud=5:plsq=on:plsqr=1,1:ss=axioms:i=672:si=on:rtra=on_0 on DTF2THF_12319 for (2951ds/672Mi)
% 36.14/6.52 % (12773)Instruction limit reached!
% 36.14/6.52 % (12773)------------------------------
% 36.14/6.52 % (12773)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.14/6.52 % (12773)Termination reason: Unknown
% 36.14/6.52 % (12773)Termination phase: Saturation
% 36.14/6.52
% 36.14/6.52 % (12773)Memory used [KB]: 9210
% 36.14/6.52 % (12773)Time elapsed: 0.214 s
% 36.14/6.52 % (12773)Instructions burned: 673 (million)
% 36.14/6.52 % (12773)------------------------------
% 36.14/6.52 % (12773)------------------------------
% 36.14/6.53 % (12774)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=1897:si=on:rtra=on_0 on DTF2THF_12319 for (2949ds/1897Mi)
% 36.48/6.65 % (12772)Instruction limit reached!
% 36.48/6.65 % (12772)------------------------------
% 36.48/6.65 % (12772)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.48/6.65 % (12772)Termination reason: Unknown
% 36.48/6.65 % (12772)Termination phase: Saturation
% 36.48/6.65
% 36.48/6.65 % (12772)Memory used [KB]: 9466
% 36.48/6.65 % (12772)Time elapsed: 0.353 s
% 36.48/6.65 % (12772)Instructions burned: 1314 (million)
% 36.48/6.65 % (12772)------------------------------
% 36.48/6.65 % (12772)------------------------------
% 36.48/6.66 % (12775)lrs+10_1:40_av=off:fde=unused:ntd=on:plsq=on:plsqc=2:plsqr=411915,1048576:sp=unary_frequency:tgt=full:i=1202:si=on:rtra=on_0 on DTF2THF_12319 for (2948ds/1202Mi)
% 36.48/6.66 % (12771)Instruction limit reached!
% 36.48/6.66 % (12771)------------------------------
% 36.48/6.66 % (12771)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.48/6.66 % (12771)Termination reason: Unknown
% 36.48/6.66 % (12771)Termination phase: Saturation
% 36.48/6.66
% 36.48/6.66 % (12771)Memory used [KB]: 5117
% 36.48/6.66 % (12771)Time elapsed: 0.407 s
% 36.48/6.66 % (12771)Instructions burned: 1323 (million)
% 36.48/6.66 % (12771)------------------------------
% 36.48/6.66 % (12771)------------------------------
% 36.48/6.67 % (12776)dis+21_1:1_au=on:cnfonf=lazy_pi_sigma_gen:hfsq=on:hfsqc=40:hfsqr=8,1:ntd=on:sos=on:sp=occurrence:ss=axioms:i=1493:si=on:rtra=on_0 on DTF2THF_12319 for (2948ds/1493Mi)
% 37.56/6.93 % (12768)Instruction limit reached!
% 37.56/6.93 % (12768)------------------------------
% 37.56/6.93 % (12768)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.56/6.93 % (12768)Termination reason: Unknown
% 37.56/6.93 % (12768)Termination phase: Saturation
% 37.56/6.93
% 37.56/6.93 % (12768)Memory used [KB]: 7675
% 37.56/6.93 % (12768)Time elapsed: 0.746 s
% 37.56/6.93 % (12768)Instructions burned: 2401 (million)
% 37.56/6.93 % (12768)------------------------------
% 37.56/6.93 % (12768)------------------------------
% 37.56/6.95 % (12777)dis+1010_3:1_av=off:fde=unused:hud=10:nwc=10.0:s2a=on:ss=axioms:i=7679:si=on:rtra=on_0 on DTF2THF_12319 for (2945ds/7679Mi)
% 37.56/7.00 % (12776)Instruction limit reached!
% 37.56/7.00 % (12776)------------------------------
% 37.56/7.00 % (12776)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.56/7.00 % (12776)Termination reason: Unknown
% 37.56/7.00 % (12776)Termination phase: Saturation
% 37.56/7.00
% 37.56/7.00 % (12776)Memory used [KB]: 6652
% 37.56/7.00 % (12776)Time elapsed: 0.336 s
% 37.56/7.00 % (12776)Instructions burned: 1493 (million)
% 37.56/7.00 % (12776)------------------------------
% 37.56/7.00 % (12776)------------------------------
% 37.56/7.01 % (12775)Instruction limit reached!
% 37.56/7.01 % (12775)------------------------------
% 37.56/7.01 % (12775)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.56/7.01 % (12775)Termination reason: Unknown
% 37.56/7.01 % (12775)Termination phase: Saturation
% 37.56/7.01
% 37.56/7.01 % (12775)Memory used [KB]: 6140
% 37.56/7.01 % (12775)Time elapsed: 0.353 s
% 37.56/7.01 % (12775)Instructions burned: 1204 (million)
% 37.56/7.01 % (12775)------------------------------
% 37.56/7.01 % (12775)------------------------------
% 37.56/7.01 % (12778)lrs+2_1:1024_anc=all:cnfonf=off:cs=on:e2e=on:nm=20:s2at=1.5:slsq=on:slsqr=1,2:spb=goal:i=340:si=on:rtra=on_0 on DTF2THF_12319 for (2944ds/340Mi)
% 37.56/7.02 % (12779)dis+1002_1:1_acc=model:au=on:nwc=5.0:sd=5:ss=axioms:st=2.5:i=3672:si=on:rtra=on_0 on DTF2THF_12319 for (2944ds/3672Mi)
% 41.38/7.12 % (12778)Instruction limit reached!
% 41.38/7.12 % (12778)------------------------------
% 41.38/7.12 % (12778)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.38/7.12 % (12778)Termination reason: Unknown
% 41.38/7.12 % (12778)Termination phase: Saturation
% 41.38/7.12
% 41.38/7.12 % (12778)Memory used [KB]: 8699
% 41.38/7.12 % (12778)Time elapsed: 0.108 s
% 41.38/7.12 % (12778)Instructions burned: 340 (million)
% 41.38/7.12 % (12778)------------------------------
% 41.38/7.12 % (12778)------------------------------
% 42.02/7.13 % (12780)dis-1002_3:1_acc=model:bd=off:bsd=on:bsdmm=1:cnfonf=lazy_not_be_gen:fd=off:fe=off:ntd=on:nwc=10.0:piset=equals:plsq=on:plsqc=1:plsqr=32,1:sp=const_max:uhcvi=on:i=1535:si=on:rtra=on_0 on DTF2THF_12319 for (2943ds/1535Mi)
% 42.02/7.14 % (12774)Instruction limit reached!
% 42.02/7.14 % (12774)------------------------------
% 42.02/7.14 % (12774)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.02/7.14 % (12774)Termination reason: Unknown
% 42.02/7.14 % (12774)Termination phase: Saturation
% 42.02/7.14
% 42.02/7.14 % (12774)Memory used [KB]: 11641
% 42.02/7.14 % (12774)Time elapsed: 0.607 s
% 42.02/7.14 % (12774)Instructions burned: 1898 (million)
% 42.02/7.14 % (12774)------------------------------
% 42.02/7.14 % (12774)------------------------------
% 42.02/7.15 % (12781)dis+10_16:1_hud=1:plsq=on:plsqc=1:plsqr=32,1:prag=on:sd=1:sgt=64:ss=axioms:i=4637:si=on:rtra=on_0 on DTF2THF_12319 for (2943ds/4637Mi)
% 43.15/7.40 % (12748)Refutation not found, non-redundant clauses discarded% (12748)------------------------------
% 43.15/7.40 % (12748)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.15/7.40 % (12748)Termination reason: Refutation not found, non-redundant clauses discarded
% 43.15/7.40
% 43.15/7.40 % (12748)Memory used [KB]: 10874
% 43.15/7.40 % (12748)Time elapsed: 1.959 s
% 43.15/7.40 % (12748)Instructions burned: 6344 (million)
% 43.15/7.40 % (12748)------------------------------
% 43.15/7.40 % (12748)------------------------------
% 43.15/7.41 % (12782)lrs+10_1:1_fde=unused:prag=on:sd=2:sgt=32:ss=axioms:i=3174:si=on:rtra=on_0 on DTF2THF_12319 for (2940ds/3174Mi)
% 43.47/7.51 % (12780)Instruction limit reached!
% 43.47/7.51 % (12780)------------------------------
% 43.47/7.51 % (12780)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.47/7.51 % (12780)Termination reason: Unknown
% 43.47/7.51 % (12780)Termination phase: Saturation
% 43.47/7.51
% 43.47/7.51 % (12780)Memory used [KB]: 11257
% 43.47/7.51 % (12780)Time elapsed: 0.386 s
% 43.47/7.51 % (12780)Instructions burned: 1537 (million)
% 43.47/7.51 % (12780)------------------------------
% 43.47/7.51 % (12780)------------------------------
% 43.47/7.52 % (12783)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=307:si=on:rtra=on_0 on DTF2THF_12319 for (2939ds/307Mi)
% 43.47/7.60 % (12783)Instruction limit reached!
% 43.47/7.60 % (12783)------------------------------
% 43.47/7.60 % (12783)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.47/7.60 % (12783)Termination reason: Unknown
% 43.47/7.60 % (12783)Termination phase: Saturation
% 43.47/7.60
% 43.47/7.60 % (12783)Memory used [KB]: 6524
% 43.47/7.60 % (12783)Time elapsed: 0.076 s
% 43.47/7.60 % (12783)Instructions burned: 311 (million)
% 43.47/7.60 % (12783)------------------------------
% 43.47/7.60 % (12783)------------------------------
% 44.16/7.61 % (12784)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=3619:si=on:rtra=on_0 on DTF2THF_12319 for (2938ds/3619Mi)
% 44.16/7.61 % (12767)Instruction limit reached!
% 44.16/7.61 % (12767)------------------------------
% 44.16/7.61 % (12767)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 44.16/7.61 % (12767)Termination reason: Unknown
% 44.16/7.61 % (12767)Termination phase: Saturation
% 44.16/7.61
% 44.16/7.61 % (12767)Memory used [KB]: 9083
% 44.16/7.61 % (12767)Time elapsed: 1.448 s
% 44.16/7.61 % (12767)Instructions burned: 5061 (million)
% 44.16/7.61 % (12767)------------------------------
% 44.16/7.61 % (12767)------------------------------
% 44.16/7.62 % (12785)lrs+1002_1:1_au=on:cbe=off:fde=none:ins=1:sp=const_max:i=2325:si=on:rtra=on_0 on DTF2THF_12319 for (2938ds/2325Mi)
% 48.41/8.03 % (12769)Instruction limit reached!
% 48.41/8.03 % (12769)------------------------------
% 48.41/8.03 % (12769)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 48.41/8.03 % (12769)Termination reason: Unknown
% 48.41/8.03 % (12769)Termination phase: Saturation
% 48.41/8.03
% 48.41/8.03 % (12769)Memory used [KB]: 12792
% 48.41/8.03 % (12769)Time elapsed: 1.823 s
% 48.41/8.03 % (12769)Instructions burned: 5800 (million)
% 48.41/8.03 % (12769)------------------------------
% 48.41/8.03 % (12769)------------------------------
% 48.41/8.04 % (12786)dis+1002_1:1_au=on:sac=on:sd=5:slsq=on:slsqr=1,4:ss=axioms:st=2.0:i=2341:si=on:rtra=on_0 on DTF2THF_12319 for (2934ds/2341Mi)
% 49.51/8.20 % (12779)Instruction limit reached!
% 49.51/8.20 % (12779)------------------------------
% 49.51/8.20 % (12779)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 49.51/8.20 % (12779)Termination reason: Unknown
% 49.51/8.20 % (12779)Termination phase: Saturation
% 49.51/8.20
% 49.51/8.20 % (12779)Memory used [KB]: 11257
% 49.51/8.20 % (12779)Time elapsed: 1.182 s
% 49.51/8.20 % (12779)Instructions burned: 3674 (million)
% 49.51/8.20 % (12779)------------------------------
% 49.51/8.20 % (12779)------------------------------
% 49.51/8.21 % (12787)lrs+1010_1:16_apa=on:bsd=on:cnfonf=off:hud=10:sac=on:sos=on:ss=axioms:i=7257:si=on:rtra=on_0 on DTF2THF_12319 for (2932ds/7257Mi)
% 50.02/8.34 % (12785)Instruction limit reached!
% 50.02/8.34 % (12785)------------------------------
% 50.02/8.34 % (12785)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.02/8.34 % (12785)Termination reason: Unknown
% 50.02/8.34 % (12785)Termination phase: Saturation
% 50.02/8.34
% 50.02/8.34 % (12785)Memory used [KB]: 14839
% 50.02/8.34 % (12785)Time elapsed: 0.745 s
% 50.02/8.34 % (12785)Instructions burned: 2327 (million)
% 50.02/8.34 % (12785)------------------------------
% 50.02/8.34 % (12785)------------------------------
% 50.02/8.35 % (12788)ott+1010_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=3548551,65536:s2a=on:i=3710:si=on:rtra=on_0 on DTF2THF_12319 for (2931ds/3710Mi)
% 50.49/8.40 % (12782)Instruction limit reached!
% 50.49/8.40 % (12782)------------------------------
% 50.49/8.40 % (12782)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.49/8.40 % (12782)Termination reason: Unknown
% 50.49/8.40 % (12782)Termination phase: Saturation
% 50.49/8.40
% 50.49/8.40 % (12782)Memory used [KB]: 15735
% 50.49/8.40 % (12782)Time elapsed: 0.987 s
% 50.49/8.40 % (12782)Instructions burned: 3176 (million)
% 50.49/8.40 % (12782)------------------------------
% 50.49/8.40 % (12782)------------------------------
% 50.49/8.41 % (12789)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=326:si=on:rtra=on_0 on DTF2THF_12319 for (2930ds/326Mi)
% 50.79/8.51 % (12789)Instruction limit reached!
% 50.79/8.51 % (12789)------------------------------
% 50.79/8.51 % (12789)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.79/8.51 % (12789)Termination reason: Unknown
% 50.79/8.51 % (12789)Termination phase: Saturation
% 50.79/8.51
% 50.79/8.51 % (12789)Memory used [KB]: 7419
% 50.79/8.51 % (12789)Time elapsed: 0.103 s
% 50.79/8.51 % (12789)Instructions burned: 328 (million)
% 50.79/8.51 % (12789)------------------------------
% 50.79/8.51 % (12789)------------------------------
% 50.79/8.52 % (12790)lrs+1010_1:64_au=on:c=on:e2e=on:flr=on:hfsq=on:hfsql=off:hfsqr=4,1:ins=1:ntd=on:sp=occurrence:i=1100:si=on:rtra=on_0 on DTF2THF_12319 for (2929ds/1100Mi)
% 51.20/8.63 % (12781)Instruction limit reached!
% 51.20/8.63 % (12781)------------------------------
% 51.20/8.63 % (12781)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 51.20/8.63 % (12781)Termination reason: Unknown
% 51.20/8.63 % (12781)Termination phase: Saturation
% 51.20/8.63
% 51.20/8.63 % (12781)Memory used [KB]: 10490
% 51.20/8.63 % (12781)Time elapsed: 1.486 s
% 51.20/8.63 % (12781)Instructions burned: 4638 (million)
% 51.20/8.63 % (12781)------------------------------
% 51.20/8.63 % (12781)------------------------------
% 51.20/8.64 % (12791)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_12319 for (2928ds/406Mi)
% 51.20/8.67 % (12784)Instruction limit reached!
% 51.20/8.67 % (12784)------------------------------
% 51.20/8.67 % (12784)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 51.20/8.67 % (12784)Termination reason: Unknown
% 51.20/8.67 % (12784)Termination phase: Saturation
% 51.20/8.67
% 51.20/8.67 % (12784)Memory used [KB]: 14200
% 51.20/8.67 % (12784)Time elapsed: 1.063 s
% 51.20/8.67 % (12784)Instructions burned: 3620 (million)
% 51.20/8.67 % (12784)------------------------------
% 51.20/8.67 % (12784)------------------------------
% 51.20/8.68 % (12792)dis+1010_1:1_aac=none:bd=preordered:e2e=on:fde=none:fe=axiom:nm=16:nwc=10.0:prag=on:i=1871:si=on:rtra=on_0 on DTF2THF_12319 for (2927ds/1871Mi)
% 51.43/8.76 % (12791)Instruction limit reached!
% 51.43/8.76 % (12791)------------------------------
% 51.43/8.76 % (12791)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 51.43/8.76 % (12791)Termination reason: Unknown
% 51.43/8.76 % (12791)Termination phase: Saturation
% 51.43/8.76
% 51.43/8.76 % (12791)Memory used [KB]: 7291
% 51.43/8.76 % (12791)Time elapsed: 0.123 s
% 51.43/8.76 % (12791)Instructions burned: 409 (million)
% 51.43/8.76 % (12791)------------------------------
% 51.43/8.76 % (12791)------------------------------
% 51.43/8.77 % (12793)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=1194:si=on:rtra=on_0 on DTF2THF_12319 for (2926ds/1194Mi)
% 51.43/8.79 % (12786)Instruction limit reached!
% 51.43/8.79 % (12786)------------------------------
% 51.43/8.79 % (12786)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 51.43/8.79 % (12786)Termination reason: Unknown
% 51.43/8.79 % (12786)Termination phase: Saturation
% 51.43/8.79
% 51.43/8.79 % (12786)Memory used [KB]: 9594
% 51.43/8.79 % (12786)Time elapsed: 0.752 s
% 51.43/8.79 % (12786)Instructions burned: 2341 (million)
% 51.43/8.79 % (12786)------------------------------
% 51.43/8.79 % (12786)------------------------------
% 52.42/8.80 % (12794)dis+10_1:1024_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=32,1:spb=goal_then_units:i=474:si=on:rtra=on_0 on DTF2THF_12319 for (2926ds/474Mi)
% 52.42/8.87 % (12790)Instruction limit reached!
% 52.42/8.87 % (12790)------------------------------
% 52.42/8.87 % (12790)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 52.42/8.87 % (12790)Termination reason: Unknown
% 52.42/8.87 % (12790)Termination phase: Saturation
% 52.42/8.87
% 52.42/8.87 % (12790)Memory used [KB]: 11257
% 52.42/8.87 % (12790)Time elapsed: 0.351 s
% 52.42/8.87 % (12790)Instructions burned: 1102 (million)
% 52.42/8.87 % (12790)------------------------------
% 52.42/8.87 % (12790)------------------------------
% 52.42/8.88 % (12795)dis+1010_1:1_au=on:cnfonf=lazy_gen:ins=3:plsq=on:plsqc=1:plsqr=15142123,262144:sp=reverse_arity:i=3115:si=on:rtra=on_0 on DTF2THF_12319 for (2925ds/3115Mi)
% 52.89/8.92 % (12794)Instruction limit reached!
% 52.89/8.92 % (12794)------------------------------
% 52.89/8.92 % (12794)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 52.89/8.92 % (12794)Termination reason: Unknown
% 52.89/8.92 % (12794)Termination phase: Saturation
% 52.89/8.92
% 52.89/8.92 % (12794)Memory used [KB]: 9083
% 52.89/8.92 % (12794)Time elapsed: 0.114 s
% 52.89/8.92 % (12794)Instructions burned: 476 (million)
% 52.89/8.92 % (12794)------------------------------
% 52.89/8.92 % (12794)------------------------------
% 52.89/8.93 % (12796)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=831:si=on:rtra=on_0 on DTF2THF_12319 for (2925ds/831Mi)
% 56.17/9.15 % (12793)Instruction limit reached!
% 56.17/9.15 % (12793)------------------------------
% 56.17/9.15 % (12793)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.17/9.15 % (12793)Termination reason: Unknown
% 56.17/9.15 % (12793)Termination phase: Saturation
% 56.17/9.15
% 56.17/9.15 % (12793)Memory used [KB]: 9978
% 56.17/9.15 % (12793)Time elapsed: 0.375 s
% 56.17/9.15 % (12793)Instructions burned: 1194 (million)
% 56.17/9.15 % (12793)------------------------------
% 56.17/9.15 % (12793)------------------------------
% 56.17/9.16 % (12797)dis+1666_14:1_cnfonf=lazy_gen:fe=off:hud=10:piset=all_but_not_eq:prag=on:sp=const_max:i=1188:si=on:rtra=on_0 on DTF2THF_12319 for (2923ds/1188Mi)
% 56.17/9.19 % (12796)Instruction limit reached!
% 56.17/9.19 % (12796)------------------------------
% 56.17/9.19 % (12796)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.17/9.19 % (12796)Termination reason: Unknown
% 56.17/9.19 % (12796)Termination phase: Saturation
% 56.17/9.19
% 56.17/9.19 % (12796)Memory used [KB]: 8187
% 56.17/9.19 % (12796)Time elapsed: 0.263 s
% 56.17/9.19 % (12796)Instructions burned: 832 (million)
% 56.17/9.19 % (12796)------------------------------
% 56.17/9.19 % (12796)------------------------------
% 56.64/9.20 % (12798)ott+1010_1:20_cnfonf=lazy_pi_sigma_gen:fe=axiom:plsq=on:plsqc=2:plsqr=32,1:sac=on:sos=all:i=2868:si=on:rtra=on_0 on DTF2THF_12319 for (2922ds/2868Mi)
% 56.64/9.27 % (12792)Instruction limit reached!
% 56.64/9.27 % (12792)------------------------------
% 56.64/9.27 % (12792)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.64/9.27 % (12792)Termination reason: Unknown
% 56.64/9.27 % (12792)Termination phase: Saturation
% 56.64/9.27
% 56.64/9.27 % (12792)Memory used [KB]: 14839
% 56.64/9.27 % (12792)Time elapsed: 0.594 s
% 56.64/9.27 % (12792)Instructions burned: 1873 (million)
% 56.64/9.27 % (12792)------------------------------
% 56.64/9.27 % (12792)------------------------------
% 56.64/9.28 % (12788)Instruction limit reached!
% 56.64/9.28 % (12788)------------------------------
% 56.64/9.28 % (12788)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.64/9.28 % (12788)Termination reason: Unknown
% 56.64/9.28 % (12788)Termination phase: Saturation
% 56.64/9.28
% 56.64/9.28 % (12788)Memory used [KB]: 9978
% 56.64/9.28 % (12788)Time elapsed: 0.924 s
% 56.64/9.28 % (12788)Instructions burned: 3710 (million)
% 56.64/9.28 % (12788)------------------------------
% 56.64/9.28 % (12788)------------------------------
% 56.64/9.28 % (12799)dis+10_1:4_atotf=0.1:avsq=on:bsr=unit_only:e2e=on:sd=1:sp=const_max:ss=axioms:i=1516:si=on:rtra=on_0 on DTF2THF_12319 for (2921ds/1516Mi)
% 56.64/9.29 % (12800)lrs+1002_1:20_afp=1000:au=on:bsd=on:cnfonf=lazy_not_gen_be_off:sos=all:sp=const_max:i=2321:si=on:rtra=on_0 on DTF2THF_12319 for (2921ds/2321Mi)
% 57.12/9.33 % (12777)Instruction limit reached!
% 57.12/9.33 % (12777)------------------------------
% 57.12/9.33 % (12777)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 57.12/9.33 % (12777)Termination reason: Unknown
% 57.12/9.33 % (12777)Termination phase: Saturation
% 57.12/9.33
% 57.12/9.33 % (12777)Memory used [KB]: 15351
% 57.12/9.33 % (12777)Time elapsed: 2.387 s
% 57.12/9.33 % (12777)Instructions burned: 7679 (million)
% 57.12/9.33 % (12777)------------------------------
% 57.12/9.33 % (12777)------------------------------
% 57.12/9.34 % (12801)dis+1010_1:1_au=on:bd=off:bsd=on:ixr=off:sp=const_max:i=2812:si=on:rtra=on_0 on DTF2THF_12319 for (2921ds/2812Mi)
% 57.37/9.45 % (12797)Instruction limit reached!
% 57.37/9.45 % (12797)------------------------------
% 57.37/9.45 % (12797)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 57.37/9.45 % (12797)Termination reason: Unknown
% 57.37/9.45 % (12797)Termination phase: Saturation
% 57.37/9.45
% 57.37/9.45 % (12797)Memory used [KB]: 9850
% 57.37/9.45 % (12797)Time elapsed: 0.294 s
% 57.37/9.45 % (12797)Instructions burned: 1188 (million)
% 57.37/9.45 % (12797)------------------------------
% 57.37/9.45 % (12797)------------------------------
% 57.37/9.46 % (12802)dis+1002_8:1_bd=off:sd=1:sgt=16:ss=axioms:i=4604:si=on:rtra=on_0 on DTF2THF_12319 for (2920ds/4604Mi)
% 58.07/9.60 % (12795)Instruction limit reached!
% 58.07/9.60 % (12795)------------------------------
% 58.07/9.60 % (12795)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 58.07/9.60 % (12795)Termination reason: Unknown
% 58.07/9.60 % (12795)Termination phase: Saturation
% 58.07/9.60
% 58.07/9.60 % (12795)Memory used [KB]: 8955
% 58.07/9.60 % (12795)Time elapsed: 0.724 s
% 58.07/9.60 % (12795)Instructions burned: 3118 (million)
% 58.07/9.60 % (12795)------------------------------
% 58.07/9.60 % (12795)------------------------------
% 58.07/9.61 % (12803)ott+1002_1:4_c=on:chr=on:cnfonf=lazy_not_be_gen:hud=10:nm=10:piset=all_but_not_eq:rp=on:spb=goal:uhcvi=on:i=2678:si=on:rtra=on_0 on DTF2THF_12319 for (2918ds/2678Mi)
% 58.20/9.75 % (12799)Instruction limit reached!
% 58.20/9.75 % (12799)------------------------------
% 58.20/9.75 % (12799)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 58.20/9.75 % (12799)Termination reason: Unknown
% 58.20/9.75 % (12799)Termination phase: Saturation
% 58.20/9.75
% 58.20/9.75 % (12799)Memory used [KB]: 10746
% 58.20/9.75 % (12799)Time elapsed: 0.466 s
% 58.20/9.75 % (12799)Instructions burned: 1516 (million)
% 58.20/9.75 % (12799)------------------------------
% 58.20/9.75 % (12799)------------------------------
% 58.20/9.76 % (12804)dis+1010_1:4_avsq=on:avsqr=16,1:bet=on:cbe=off:cnfonf=lazy_not_be_gen:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=643:si=on:rtra=on_0 on DTF2THF_12319 for (2917ds/643Mi)
% 58.77/9.85 % (12800)Instruction limit reached!
% 58.77/9.85 % (12800)------------------------------
% 58.77/9.85 % (12800)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 58.77/9.85 % (12800)Termination reason: Unknown
% 58.77/9.85 % (12800)Termination phase: Saturation
% 58.77/9.85
% 58.77/9.85 % (12800)Memory used [KB]: 9594
% 58.77/9.85 % (12800)Time elapsed: 0.567 s
% 58.77/9.85 % (12800)Instructions burned: 2323 (million)
% 58.77/9.85 % (12800)------------------------------
% 58.77/9.85 % (12800)------------------------------
% 58.77/9.86 % (12805)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=458:si=on:rtra=on_0 on DTF2THF_12319 for (2916ds/458Mi)
% 59.44/9.91 % (12798)Instruction limit reached!
% 59.44/9.91 % (12798)------------------------------
% 59.44/9.91 % (12798)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 59.44/9.91 % (12798)Termination reason: Unknown
% 59.44/9.91 % (12798)Termination phase: Saturation
% 59.44/9.91
% 59.44/9.91 % (12798)Memory used [KB]: 7291
% 59.44/9.91 % (12798)Time elapsed: 0.710 s
% 59.44/9.91 % (12798)Instructions burned: 2872 (million)
% 59.44/9.91 % (12798)------------------------------
% 59.44/9.91 % (12798)------------------------------
% 59.44/9.91 % (12804)Instruction limit reached!
% 59.44/9.91 % (12804)------------------------------
% 59.44/9.91 % (12804)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 59.44/9.91 % (12804)Termination reason: Unknown
% 59.44/9.91 % (12804)Termination phase: Saturation
% 59.44/9.91
% 59.44/9.91 % (12804)Memory used [KB]: 8699
% 59.44/9.91 % (12804)Time elapsed: 0.155 s
% 59.44/9.91 % (12804)Instructions burned: 645 (million)
% 59.44/9.91 % (12804)------------------------------
% 59.44/9.91 % (12804)------------------------------
% 59.44/9.92 % (12806)lrs+1010_1:1_anc=all_dependent:apa=on:au=on:bd=off:c=on:cnfonf=off:ntd=on:i=2546:si=on:rtra=on_0 on DTF2THF_12319 for (2915ds/2546Mi)
% 59.44/9.92 % (12807)dis+21_1:1_acc=model:au=on:cnfonf=lazy_gen:ins=2:plsq=on:plsqc=1:plsqr=32,1:i=1432:si=on:rtra=on_0 on DTF2THF_12319 for (2915ds/1432Mi)
% 59.44/9.97 % (12805)Instruction limit reached!
% 59.44/9.97 % (12805)------------------------------
% 59.44/9.97 % (12805)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 59.44/9.97 % (12805)Termination reason: Unknown
% 59.44/9.97 % (12805)Termination phase: Saturation
% 59.44/9.97
% 59.44/9.97 % (12805)Memory used [KB]: 8699
% 59.44/9.97 % (12805)Time elapsed: 0.114 s
% 59.44/9.97 % (12805)Instructions burned: 460 (million)
% 59.44/9.97 % (12805)------------------------------
% 59.44/9.97 % (12805)------------------------------
% 59.44/9.98 % (12808)dis+1002_1:1_cnfonf=lazy_not_gen:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=386:si=on:rtra=on_0 on DTF2THF_12319 for (2914ds/386Mi)
% 62.48/10.08 % (12808)Instruction limit reached!
% 62.48/10.08 % (12808)------------------------------
% 62.48/10.08 % (12808)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 62.48/10.08 % (12808)Termination reason: Unknown
% 62.48/10.08 % (12808)Termination phase: Saturation
% 62.48/10.08
% 62.48/10.08 % (12808)Memory used [KB]: 6524
% 62.48/10.08 % (12808)Time elapsed: 0.092 s
% 62.48/10.08 % (12808)Instructions burned: 388 (million)
% 62.48/10.08 % (12808)------------------------------
% 62.48/10.08 % (12808)------------------------------
% 62.48/10.09 % (12809)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=360:si=on:rtra=on_0 on DTF2THF_12319 for (2913ds/360Mi)
% 63.16/10.17 % (12809)Instruction limit reached!
% 63.16/10.17 % (12809)------------------------------
% 63.16/10.17 % (12809)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 63.16/10.17 % (12809)Termination reason: Unknown
% 63.16/10.17 % (12809)Termination phase: Saturation
% 63.16/10.17
% 63.16/10.17 % (12809)Memory used [KB]: 6524
% 63.16/10.17 % (12809)Time elapsed: 0.087 s
% 63.16/10.17 % (12809)Instructions burned: 363 (million)
% 63.16/10.17 % (12809)------------------------------
% 63.16/10.17 % (12809)------------------------------
% 63.16/10.18 % (12810)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=5446:si=on:rtra=on_0 on DTF2THF_12319 for (2912ds/5446Mi)
% 63.68/10.23 % (12801)Instruction limit reached!
% 63.68/10.23 % (12801)------------------------------
% 63.68/10.23 % (12801)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 63.68/10.23 % (12801)Termination reason: Unknown
% 63.68/10.23 % (12801)Termination phase: Saturation
% 63.68/10.23
% 63.68/10.23 % (12801)Memory used [KB]: 11001
% 63.68/10.23 % (12801)Time elapsed: 0.894 s
% 63.68/10.23 % (12801)Instructions burned: 2814 (million)
% 63.68/10.23 % (12801)------------------------------
% 63.68/10.23 % (12801)------------------------------
% 63.68/10.24 % (12811)dis+10_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=2573:si=on:rtra=on_0 on DTF2THF_12319 for (2912ds/2573Mi)
% 63.68/10.25 % (12807)Instruction limit reached!
% 63.68/10.25 % (12807)------------------------------
% 63.68/10.25 % (12807)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 63.68/10.25 % (12807)Termination reason: Unknown
% 63.68/10.25 % (12807)Termination phase: Saturation
% 63.68/10.25
% 63.68/10.25 % (12807)Memory used [KB]: 12025
% 63.68/10.25 % (12807)Time elapsed: 0.330 s
% 63.68/10.25 % (12807)Instructions burned: 1434 (million)
% 63.68/10.25 % (12807)------------------------------
% 63.68/10.25 % (12807)------------------------------
% 63.68/10.26 % (12812)lrs+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:tnu=1:i=2655:si=on:rtra=on_0 on DTF2THF_12319 for (2912ds/2655Mi)
% 63.68/10.28 % (12803)Instruction limit reached!
% 63.68/10.28 % (12803)------------------------------
% 63.68/10.28 % (12803)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 63.68/10.28 % (12803)Termination reason: Unknown
% 63.68/10.28 % (12803)Termination phase: Saturation
% 63.68/10.28
% 63.68/10.28 % (12803)Memory used [KB]: 11001
% 63.68/10.28 % (12803)Time elapsed: 0.665 s
% 63.68/10.28 % (12803)Instructions burned: 2679 (million)
% 63.68/10.28 % (12803)------------------------------
% 63.68/10.28 % (12803)------------------------------
% 63.68/10.29 % (12813)dis+1002_16:1_apa=on:au=on:av=off:cnfonf=off:e2e=on:nm=0:nwc=10.0:i=2781:si=on:rtra=on_0 on DTF2THF_12319 for (2911ds/2781Mi)
% 64.49/10.43 % (12787)Instruction limit reached!
% 64.49/10.43 % (12787)------------------------------
% 64.49/10.43 % (12787)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 64.49/10.43 % (12787)Termination reason: Unknown
% 64.49/10.43 % (12787)Termination phase: Saturation
% 64.49/10.43
% 64.49/10.43 % (12787)Memory used [KB]: 9978
% 64.49/10.43 % (12787)Time elapsed: 2.221 s
% 64.49/10.43 % (12787)Instructions burned: 7258 (million)
% 64.49/10.43 % (12787)------------------------------
% 64.49/10.43 % (12787)------------------------------
% 64.49/10.44 % (12814)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=307:si=on:rtra=on_0 on DTF2THF_12319 for (2910ds/307Mi)
% 64.73/10.52 % (12814)Instruction limit reached!
% 64.73/10.52 % (12814)------------------------------
% 64.73/10.52 % (12814)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 64.73/10.52 % (12814)Termination reason: Unknown
% 64.73/10.52 % (12814)Termination phase: Saturation
% 64.73/10.52
% 64.73/10.52 % (12814)Memory used [KB]: 6524
% 64.73/10.52 % (12814)Time elapsed: 0.078 s
% 64.73/10.52 % (12814)Instructions burned: 308 (million)
% 64.73/10.52 % (12814)------------------------------
% 64.73/10.52 % (12814)------------------------------
% 64.73/10.52 % (12815)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=1548:si=on:rtra=on_0 on DTF2THF_12319 for (2909ds/1548Mi)
% 65.01/10.70 % (12806)Instruction limit reached!
% 65.01/10.70 % (12806)------------------------------
% 65.01/10.70 % (12806)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 65.01/10.70 % (12806)Termination reason: Unknown
% 65.01/10.70 % (12806)Termination phase: Saturation
% 65.01/10.70
% 65.01/10.70 % (12806)Memory used [KB]: 10362
% 65.01/10.70 % (12806)Time elapsed: 0.780 s
% 65.01/10.70 % (12806)Instructions burned: 2548 (million)
% 65.01/10.70 % (12806)------------------------------
% 65.01/10.70 % (12806)------------------------------
% 64.43/10.71 % (12816)lrs+10_1:3_alpa=true:hud=3:ins=1:ntd=on:plsq=on:plsqc=1:plsqr=32,1:prag=on:s2a=on:s2agt=10:i=5214:si=on:rtra=on_0 on DTF2THF_12319 for (2907ds/5214Mi)
% 65.33/10.87 % (12811)Instruction limit reached!
% 65.33/10.87 % (12811)------------------------------
% 65.33/10.87 % (12811)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 65.33/10.87 % (12811)Termination reason: Unknown
% 65.33/10.87 % (12811)Termination phase: Saturation
% 65.33/10.87
% 65.33/10.87 % (12811)Memory used [KB]: 9850
% 65.33/10.87 % (12811)Time elapsed: 0.652 s
% 65.33/10.87 % (12811)Instructions burned: 2576 (million)
% 65.33/10.87 % (12811)------------------------------
% 65.33/10.87 % (12811)------------------------------
% 65.33/10.88 % (12817)dis+21_1:1_aac=none:bsr=on:nwc=3.0:s2a=on:i=3201:si=on:rtra=on_0 on DTF2THF_12319 for (2905ds/3201Mi)
% 66.07/10.91 % (12802)Instruction limit reached!
% 66.07/10.91 % (12802)------------------------------
% 66.07/10.91 % (12802)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 66.07/10.91 % (12802)Termination reason: Unknown
% 66.07/10.91 % (12802)Termination phase: Saturation
% 66.07/10.91
% 66.07/10.91 % (12802)Memory used [KB]: 13304
% 66.07/10.91 % (12802)Time elapsed: 1.448 s
% 66.07/10.91 % (12802)Instructions burned: 4605 (million)
% 66.07/10.91 % (12802)------------------------------
% 66.07/10.91 % (12802)------------------------------
% 66.07/10.91 % (12812)Instruction limit reached!
% 66.07/10.91 % (12812)------------------------------
% 66.07/10.91 % (12812)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 66.07/10.91 % (12812)Termination reason: Unknown
% 66.07/10.91 % (12812)Termination phase: Saturation
% 66.07/10.91
% 66.07/10.91 % (12812)Memory used [KB]: 3965
% 66.07/10.91 % (12812)Time elapsed: 0.677 s
% 66.07/10.91 % (12812)Instructions burned: 2657 (million)
% 66.07/10.91 % (12812)------------------------------
% 66.07/10.91 % (12812)------------------------------
% 66.07/10.92 % (12818)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=454:si=on:rtra=on_0 on DTF2THF_12319 for (2905ds/454Mi)
% 66.07/10.92 % (12819)lrs+1002_1:32_au=on:ins=2:nm=16:ntd=on:piset=all_but_not_eq:sp=occurrence:i=3049:si=on:rtra=on_0 on DTF2THF_12319 for (2905ds/3049Mi)
% 66.07/11.00 % (12815)Instruction limit reached!
% 66.07/11.00 % (12815)------------------------------
% 66.07/11.00 % (12815)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 66.07/11.00 % (12815)Termination reason: Unknown
% 66.07/11.00 % (12815)Termination phase: Saturation
% 66.07/11.00
% 66.07/11.00 % (12815)Memory used [KB]: 9978
% 66.07/11.00 % (12815)Time elapsed: 0.472 s
% 66.07/11.00 % (12815)Instructions burned: 1549 (million)
% 66.07/11.00 % (12815)------------------------------
% 66.07/11.00 % (12815)------------------------------
% 66.07/11.01 % (12820)lrs+1010_1:1_bd=preordered:cnfonf=off:e2e=on:kws=inv_precedence:lwlo=on:sd=2:ss=axioms:i=7311:si=on:rtra=on_0 on DTF2THF_12319 for (2904ds/7311Mi)
% 69.41/11.03 % (12818)Instruction limit reached!
% 69.41/11.03 % (12818)------------------------------
% 69.41/11.03 % (12818)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 69.41/11.03 % (12818)Termination reason: Unknown
% 69.41/11.03 % (12818)Termination phase: Saturation
% 69.41/11.03
% 69.41/11.03 % (12818)Memory used [KB]: 13432
% 69.41/11.03 % (12818)Time elapsed: 0.113 s
% 69.41/11.03 % (12818)Instructions burned: 455 (million)
% 69.41/11.03 % (12818)------------------------------
% 69.41/11.03 % (12818)------------------------------
% 69.41/11.04 % (12821)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=6804:si=on:rtra=on_0 on DTF2THF_12319 for (2904ds/6804Mi)
% 69.95/11.14 % (12813)Instruction limit reached!
% 69.95/11.14 % (12813)------------------------------
% 69.95/11.14 % (12813)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 69.95/11.14 % (12813)Termination reason: Unknown
% 69.95/11.14 % (12813)Termination phase: Saturation
% 69.95/11.14
% 69.95/11.14 % (12813)Memory used [KB]: 7164
% 69.95/11.14 % (12813)Time elapsed: 0.880 s
% 69.95/11.14 % (12813)Instructions burned: 2781 (million)
% 69.95/11.14 % (12813)------------------------------
% 69.95/11.14 % (12813)------------------------------
% 69.95/11.15 % (12822)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1683:si=on:rtra=on_0 on DTF2THF_12319 for (2903ds/1683Mi)
% 71.95/11.66 % (12822)Instruction limit reached!
% 71.95/11.66 % (12822)------------------------------
% 71.95/11.66 % (12822)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 71.95/11.66 % (12822)Termination reason: Unknown
% 71.95/11.66 % (12822)Termination phase: Saturation
% 71.95/11.66
% 71.95/11.66 % (12822)Memory used [KB]: 15095
% 71.95/11.66 % (12822)Time elapsed: 0.531 s
% 71.95/11.66 % (12822)Instructions burned: 1683 (million)
% 71.95/11.66 % (12822)------------------------------
% 71.95/11.66 % (12822)------------------------------
% 71.95/11.67 % (12823)lrs+10_8:1_au=on:av=off:bd=off:cs=on:e2e=on:hfsq=on:hfsqc=50:hfsql=off:nm=0:i=4688:si=on:rtra=on_0 on DTF2THF_12319 for (2898ds/4688Mi)
% 73.26/11.85 % (12819)Instruction limit reached!
% 73.26/11.85 % (12819)------------------------------
% 73.26/11.85 % (12819)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 73.26/11.85 % (12819)Termination reason: Unknown
% 73.26/11.85 % (12819)Termination phase: Saturation
% 73.26/11.85
% 73.26/11.85 % (12819)Memory used [KB]: 9850
% 73.26/11.85 % (12819)Time elapsed: 0.926 s
% 73.26/11.85 % (12819)Instructions burned: 3050 (million)
% 73.26/11.85 % (12819)------------------------------
% 73.26/11.85 % (12819)------------------------------
% 73.26/11.86 % (12824)dis-1_1:1_amm=off:au=on:cbe=off:spb=intro:i=2207:si=on:rtra=on_0 on DTF2THF_12319 for (2896ds/2207Mi)
% 73.26/11.88 % (12816)Instruction limit reached!
% 73.26/11.88 % (12816)------------------------------
% 73.26/11.88 % (12816)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 73.26/11.88 % (12816)Termination reason: Unknown
% 73.26/11.88 % (12816)Termination phase: Saturation
% 73.26/11.88
% 73.26/11.88 % (12816)Memory used [KB]: 7931
% 73.26/11.88 % (12816)Time elapsed: 1.173 s
% 73.26/11.88 % (12816)Instructions burned: 5217 (million)
% 73.26/11.88 % (12816)------------------------------
% 73.26/11.88 % (12816)------------------------------
% 73.26/11.89 % (12825)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=8216:si=on:rtra=on_0 on DTF2THF_12319 for (2895ds/8216Mi)
% 73.63/11.91 % (12817)Instruction limit reached!
% 73.63/11.91 % (12817)------------------------------
% 73.63/11.91 % (12817)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 73.63/11.91 % (12817)Termination reason: Unknown
% 73.63/11.91 % (12817)Termination phase: Saturation
% 73.63/11.91
% 73.63/11.91 % (12817)Memory used [KB]: 10490
% 73.63/11.91 % (12817)Time elapsed: 1.027 s
% 73.63/11.91 % (12817)Instructions burned: 3201 (million)
% 73.63/11.91 % (12817)------------------------------
% 73.63/11.91 % (12817)------------------------------
% 73.63/11.92 % (12826)lrs+1010_1:1_atotf=0.5:au=on:cbe=off:cnfonf=lazy_not_be_gen:fe=off:nwc=5.0:spb=units:i=430:si=on:rtra=on_0 on DTF2THF_12319 for (2895ds/430Mi)
% 73.63/11.95 % (12810)Instruction limit reached!
% 73.63/11.95 % (12810)------------------------------
% 73.63/11.95 % (12810)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 73.63/11.95 % (12810)Termination reason: Unknown
% 73.63/11.95 % (12810)Termination phase: Saturation
% 73.63/11.95
% 73.63/11.95 % (12810)Memory used [KB]: 14200
% 73.63/11.95 % (12810)Time elapsed: 1.791 s
% 73.63/11.95 % (12810)Instructions burned: 5447 (million)
% 73.63/11.95 % (12810)------------------------------
% 73.63/11.95 % (12810)------------------------------
% 73.63/11.96 % (12827)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=2012:si=on:rtra=on_0 on DTF2THF_12319 for (2895ds/2012Mi)
% 76.50/12.03 % (12826)Instruction limit reached!
% 76.50/12.03 % (12826)------------------------------
% 76.50/12.03 % (12826)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 76.50/12.03 % (12826)Termination reason: Unknown
% 76.50/12.03 % (12826)Termination phase: Saturation
% 76.50/12.03
% 76.50/12.03 % (12826)Memory used [KB]: 9210
% 76.50/12.03 % (12826)Time elapsed: 0.107 s
% 76.50/12.03 % (12826)Instructions burned: 432 (million)
% 76.50/12.03 % (12826)------------------------------
% 76.50/12.03 % (12826)------------------------------
% 76.50/12.04 % (12828)ott+1010_1:32_apa=on:atotf=0.3:au=on:c=on:cnfonf=off:fe=off:fsr=off:nm=6:piset=or:sac=on:sos=on:i=631:si=on:rtra=on_0 on DTF2THF_12319 for (2894ds/631Mi)
% 77.59/12.23 % (12828)Instruction limit reached!
% 77.59/12.23 % (12828)------------------------------
% 77.59/12.23 % (12828)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 77.59/12.23 % (12828)Termination reason: Unknown
% 77.59/12.23 % (12828)Termination phase: Saturation
% 77.59/12.23
% 77.59/12.23 % (12828)Memory used [KB]: 6908
% 77.59/12.23 % (12828)Time elapsed: 0.220 s
% 77.59/12.23 % (12828)Instructions burned: 631 (million)
% 77.59/12.23 % (12828)------------------------------
% 77.59/12.23 % (12828)------------------------------
% 77.59/12.24 % (12829)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=8785:si=on:rtra=on_0 on DTF2THF_12319 for (2892ds/8785Mi)
% 78.40/12.31 % (12821)First to succeed.
% 78.40/12.31 % (12821)Refutation found. Thanks to Tanya!
% 78.40/12.31 % SZS status Theorem for DTF2THF_12319
% 78.40/12.31 % SZS output start Proof for DTF2THF_12319
% 78.40/12.31 thf(func_def_0, type, in: $i > $i > $o).
% 78.40/12.31 thf(func_def_1, type, exu: ($i > $o) > $o).
% 78.40/12.31 thf(func_def_6, type, setadjoin: $i > $i > $i).
% 78.40/12.31 thf(func_def_8, type, powerset: $i > $i).
% 78.40/12.31 thf(func_def_10, type, setunion: $i > $i).
% 78.40/12.31 thf(func_def_19, type, descr: ($i > $o) > $i).
% 78.40/12.31 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i).
% 78.40/12.31 thf(func_def_26, type, prop2set: $o > $i).
% 78.40/12.31 thf(func_def_36, type, nonempty: $i > $o).
% 78.40/12.31 thf(func_def_69, type, set2prop: $i > $o).
% 78.40/12.31 thf(func_def_88, type, subset: $i > $i > $o).
% 78.40/12.31 thf(func_def_89, type, disjoint: $i > $i > $o).
% 78.40/12.31 thf(func_def_90, type, setsmeet: $i > $i > $o).
% 78.40/12.31 thf(func_def_114, type, binunion: $i > $i > $i).
% 78.40/12.31 thf(func_def_122, type, binintersect: $i > $i > $i).
% 78.40/12.31 thf(func_def_135, type, regular: $i > $o).
% 78.40/12.31 thf(func_def_136, type, setminus: $i > $i > $i).
% 78.40/12.31 thf(func_def_147, type, symdiff: $i > $i > $i).
% 78.40/12.31 thf(func_def_153, type, iskpair: $i > $o).
% 78.40/12.31 thf(func_def_158, type, kpair: $i > $i > $i).
% 78.40/12.31 thf(func_def_160, type, cartprod: $i > $i > $i).
% 78.40/12.31 thf(func_def_181, type, sP1: $i > $i > $o).
% 78.40/12.31 thf(func_def_182, type, sP2: $i > $o).
% 78.40/12.31 thf(func_def_183, type, sP3: $i > $i > $o).
% 78.40/12.31 thf(func_def_184, type, sP4: $i > $i > $o).
% 78.40/12.31 thf(func_def_185, type, sP5: $i > $i > $i > $o > $o).
% 78.40/12.31 thf(func_def_190, type, sK10: $i > $o).
% 78.40/12.31 thf(func_def_192, type, sK12: ($i > $o) > $i > $i).
% 78.40/12.31 thf(func_def_196, type, sK16: $i > $i > $i).
% 78.40/12.31 thf(func_def_200, type, sK20: $i > ($i > $o) > $i).
% 78.40/12.31 thf(func_def_201, type, sK21: $i > $o).
% 78.40/12.31 thf(func_def_203, type, sK23: $i > $i > $i).
% 78.40/12.31 thf(func_def_206, type, sK26: $i > $o).
% 78.40/12.31 thf(func_def_207, type, sK27: $i > $i).
% 78.40/12.31 thf(func_def_208, type, sK28: ($i > $o) > $i).
% 78.40/12.31 thf(func_def_217, type, sK37: $i > $i > $i).
% 78.40/12.31 thf(func_def_224, type, sK44: $i > $o).
% 78.40/12.31 thf(func_def_228, type, sK48: $i > $o).
% 78.40/12.31 thf(func_def_241, type, sK61: $i > $o).
% 78.40/12.31 thf(func_def_246, type, sK66: $i > $i > $i).
% 78.40/12.31 thf(func_def_249, type, sK69: $i > $o).
% 78.40/12.31 thf(func_def_252, type, sK72: $i > ($i > $o) > $i).
% 78.40/12.31 thf(func_def_254, type, sK74: $i > $o).
% 78.40/12.31 thf(func_def_263, type, sK83: $i > $i).
% 78.40/12.31 thf(func_def_267, type, sK87: $i > $i).
% 78.40/12.31 thf(func_def_269, type, sK89: $i > $i).
% 78.40/12.31 thf(func_def_273, type, sK93: $i > $i > $i).
% 78.40/12.31 thf(func_def_274, type, sK94: $i > $i > $o).
% 78.40/12.31 thf(func_def_276, type, sK96: $i > $i).
% 78.40/12.31 thf(func_def_277, type, sK97: $i > $i).
% 78.40/12.31 thf(func_def_278, type, sK98: $i > ($i > $i > $o) > $i).
% 78.40/12.31 thf(func_def_279, type, sK99: $i > ($i > $i > $o) > $i).
% 78.40/12.31 thf(func_def_280, type, sK100: $i > $i > ($i > $i > $o) > $i).
% 78.40/12.31 thf(func_def_283, type, sK103: $i > $o).
% 78.40/12.31 thf(func_def_286, type, sK106: $i > $o).
% 78.40/12.31 thf(func_def_301, type, sK121: $i > $o).
% 78.40/12.31 thf(func_def_321, type, sK141: $i > ($i > $o) > $i).
% 78.40/12.31 thf(func_def_322, type, sK142: $i > $o).
% 78.40/12.31 thf(func_def_327, type, sK147: $i > $o).
% 78.40/12.31 thf(func_def_330, type, sK150: $i > ($i > $o) > $i).
% 78.40/12.31 thf(func_def_331, type, sK151: $i > $o).
% 78.40/12.31 thf(func_def_353, type, sK173: $i > $o).
% 78.40/12.31 thf(func_def_355, type, sK175: ($i > $o) > $i).
% 78.40/12.31 thf(func_def_356, type, sK176: ($i > $o) > $i).
% 78.40/12.31 thf(func_def_358, type, sK178: $i > $i).
% 78.40/12.31 thf(func_def_361, type, sK181: $i > $o).
% 78.40/12.31 thf(func_def_362, type, sK182: $i > $o).
% 78.40/12.31 thf(func_def_363, type, sK183: ($i > $o) > ($i > $o) > $i > $i > $i).
% 78.40/12.31 thf(func_def_364, type, sK184: ($i > $o) > ($i > $o) > $i > $i > $i).
% 78.40/12.31 thf(func_def_381, type, sK201: ($i > $o) > ($i > $o) > $i).
% 78.40/12.31 thf(func_def_382, type, sK202: ($i > $o) > ($i > $o) > $i).
% 78.40/12.31 thf(func_def_383, type, sK203: $i > $o).
% 78.40/12.31 thf(func_def_384, type, sK204: $i > $o).
% 78.40/12.31 thf(func_def_387, type, sK207: $i > $i).
% 78.40/12.31 thf(func_def_389, type, sK209: $i > $i > $i).
% 78.40/12.31 thf(func_def_390, type, sK210: $i > $i > $i).
% 78.40/12.31 thf(func_def_391, type, sK211: $i > $i > $i).
% 78.40/12.31 thf(func_def_392, type, sK212: $i > $i > $i).
% 78.40/12.31 thf(func_def_393, type, sK213: $i > $i > $i > $i).
% 78.40/12.31 thf(func_def_394, type, sK214: $i > $i).
% 78.40/12.31 thf(func_def_395, type, sK215: $i > $i).
% 78.40/12.31 thf(func_def_396, type, sK216: $i > $i).
% 78.40/12.31 thf(func_def_397, type, sK217: $i > $i).
% 78.40/12.31 thf(func_def_398, type, sK218: $i > $i > $i > $i).
% 78.40/12.31 thf(func_def_399, type, sK219: $i > $i > $i > $i).
% 78.40/12.31 thf(func_def_400, type, sK220: $i > $i > $i).
% 78.40/12.31 thf(func_def_401, type, sK221: $i > $i > $i).
% 78.40/12.31 thf(func_def_402, type, sK222: $i > $i > $i).
% 78.40/12.31 thf(func_def_404, type, sK224: $i > $i).
% 78.40/12.31 thf(func_def_405, type, sK225: $i > $i).
% 78.40/12.31 thf(func_def_406, type, sK226: $i > $i).
% 78.40/12.31 thf(func_def_407, type, sK227: $i > $i > $i).
% 78.40/12.31 thf(func_def_411, type, sK231: $i > $o).
% 78.40/12.31 thf(func_def_417, type, sK237: $i > $i).
% 78.40/12.31 thf(func_def_452, type, sK272: $i > $o).
% 78.40/12.31 thf(func_def_455, type, sK275: ($i > $o) > $i).
% 78.40/12.31 thf(func_def_456, type, sK276: $i > $o).
% 78.40/12.31 thf(func_def_457, type, sK277: $i > $o).
% 78.40/12.31 thf(func_def_460, type, sK280: $i > ($i > $o) > $i).
% 78.40/12.31 thf(func_def_461, type, sK281: $i > $o).
% 78.40/12.31 thf(func_def_475, type, sK295: $i > $o).
% 78.40/12.31 thf(func_def_482, type, sK302: $o > $i > $i > $i).
% 78.40/12.31 thf(func_def_485, type, sK305: $i > $i > $i).
% 78.40/12.31 thf(func_def_517, type, sK337: $i > $i > $i).
% 78.40/12.31 thf(func_def_518, type, sK338: ($i > $o) > ($i > $o) > $i).
% 78.40/12.31 thf(func_def_519, type, sK339: ($i > $o) > ($i > $o) > $i).
% 78.40/12.31 thf(func_def_520, type, sK340: $i > $o).
% 78.40/12.31 thf(func_def_521, type, sK341: $i > $o).
% 78.40/12.31 thf(func_def_534, type, sK354: $i > $o).
% 78.40/12.31 thf(func_def_537, type, sK357: $i > ($i > $o) > $i).
% 78.40/12.31 thf(func_def_555, type, sK375: $i > $i).
% 78.40/12.31 thf(func_def_558, type, sK378: $i > $o).
% 78.40/12.31 thf(func_def_561, type, sK381: $i > ($i > $o) > $i).
% 78.40/12.31 thf(func_def_565, type, sK385: $i > $i > $i).
% 78.40/12.31 thf(func_def_566, type, sK386: $i > $i > $i).
% 78.40/12.31 thf(func_def_572, type, sK392: ($i > $o) > $i).
% 78.40/12.31 thf(func_def_573, type, sK393: $i > $o).
% 78.40/12.31 thf(func_def_574, type, sK394: $i > $i).
% 78.40/12.31 thf(func_def_576, type, ph396: !>[X0: $tType]:(X0)).
% 78.40/12.31 thf(f9113,plain,(
% 78.40/12.31 $false),
% 78.40/12.31 inference(avatar_sat_refutation,[status(thm)],[f8593,f8880,f9111])).
% 78.40/12.31 thf(f9111,plain,(
% 78.40/12.31 ~spl395_14),
% 78.40/12.31 inference(avatar_contradiction_clause,[status(thm)],[f9110])).
% 78.40/12.31 thf(f9110,plain,(
% 78.40/12.31 $false | ~spl395_14),
% 78.40/12.31 inference(subsumption_resolution,[status(thm)],[f9109,f1566])).
% 78.40/12.31 thf(f1566,plain,(
% 78.40/12.31 (upairsubunion = $true)),
% 78.40/12.31 inference(cnf_transformation,[status(thm)],[f834])).
% 78.40/12.31 thf(f834,plain,(
% 78.40/12.31 (subsetRefl = $true) & (symdiffIneg1 = $true) & (exuI3 = $true) & (subPowSU = $true) & (symdiffI1 = $true) & (setminusER = $true) & (setoftrueEq = $true) & (dsetconstrER = $true) & (binunionE = $true) & (nonemptyE1 = $true) & (nonemptyI = $true) & (uniqinunit = $true) & (setadjoinOr = $true) & (disjointsetsI1 = $true) & (binunionIR = $true) & (subsetE = $true) & (setminusIRneg = $true) & (exuI1 = $true) & (inCongP = $true) & (singletonsswitch = $true) & (emptyInPowerset = $true) & (foundationAx = $true) & (setadjoinIL = $true) & (wellorderingAx = $true) & (powersetsubset = $true) & (subset2powerset = $true) & (descrp = $true) & (emptysetimpfalse = $true) & (upairset2IR = $true) & (binintersectEL = $true) & (setminusI = $true) & (subsetE2 = $true) & (subsetI2 = $true) & (notequalI2 = $true) & (in__Cong = $true) & (setukpairIR = $true) & (singletoninpowerset = $true) & (kpairiskpair = $true) & (notsubsetI = $true) & (exuI2 = $true) & (exuE3e = $true) & (notinemptyset = $true) & (upairsubunion = $true) & (setunionAx = $true) & (subsetTrans = $true) & (setminusILneg = $true) & (binintersectRsub = $true) & (powersetAx = $true) & (emptyI = $true) & (quantDeMorgan2 = $true) & (omega0Ax = $true) & (upairinpowunion = $true) & (replAx = $true) & (emptysetE = $true) & (binintersectSubset1 = $true) & (omegaIndAx = $true) & (binunionRsub = $true) & (binintersectI = $true) & (prop2setE = $true) & (symdiffE = $true) & (powersetE = $true) & (setadjoinIR = $true) & (nonemptyI1 = $true) & (eqimpsubset1 = $true) & (subsetI1 = $true) & (setminusLsub = $true) & (eqimpsubset2 = $true) & (setminusSubset2 = $true) & (setunionE = $true) & (setadjoinE = $true) & (emptysetAx = $true) & (emptyinPowerset = $true) & (exuEu = $true) & (singletoninpowunion = $true) & (notinsingleton = $true) & (setunion__Cong = $true) & (subsetemptysetimpeq = $true) & (descr__Cong = $true) & (upairsetE = $true) & (prop2set2propI = $true) & (binintersectSubset5 = $true) & (setunionI = $true) & (binunionIL = $true) & (setadjoinSub2 = $true) & (powerset__Cong = $true) & (binintersectER = $true) & (prop2setI = $true) & (upairset2E = $true) & (exuE3u = $true) & (notequalI1 = $true) & (exuE1 = $true) & (setminusERneg = $true) & (setadjoinSub = $true) & (quantDeMorgan3 = $true) & (upairsetIL = $true) & (binunionEcases = $true) & (emptysetsubset = $true) & (binintersectLsub = $true) & (kpairp = $true) & (quantDeMorgan1 = $true) & (powersetE1 = $true) & (vacuousDall = $true) & (dsetconstrEL = $true) & (omega__Cong = $true) & (noeltsimpempty = $true) & (setminusEL = $true) & (setminusSubset1 = $true) & (setadjoinAx = $true) & (emptyset__Cong = $true) & (inPowerset = $true) & (omegaSAx = $true) & (dsetconstr__Cong = $true) & (emptyinunitempty = $true) & (sepInPowerset = $true) & (powersetI1 = $true) & (bs114d = $true) & (binintersectSubset2 = $true) & (setukpairIL = $true) & (setextsub = $true) & (setext = $true) & (setadjoin__Cong = $true) & (symdiffIneg2 = $true) & (powersetI = $true) & (symdiffI2 = $true) & (singletonsubset = $true) & (binintersectSubset3 = $true) & (quantDeMorgan4 = $true) & (nonemptyImpWitness = $true) & (setextAx = $true) & (setminusELneg = $true) & (dsetconstrI = $true) & (notdexE = $true) & (upairsetIR = $true) & (setbeta = $true) & (eqinunit = $true) & (emptyE1 = $true) & (exuE2 = $true) & (sepSubset = $true) & (exu__Cong = $true) & (notdallE = $true) & ((($true != (subset @ (setadjoin @ (setadjoin @ sK125 @ emptyset) @ (setadjoin @ (setadjoin @ sK125 @ (setadjoin @ sK128 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ sK126 @ sK127)))) & ((in @ sK128 @ sK127) = $true)) & ((in @ sK125 @ sK126) = $true)) & (binunionLsub = $true) & (secondinupair = $true) & (binintersectSubset4 = $true)),
% 78.40/12.31 inference(skolemisation,[status(esa),new_symbols(skolem,[sK125,sK126,sK127,sK128])],[f587,f833,f832])).
% 78.40/12.31 thf(f832,plain,(
% 78.40/12.31 ? [X0 : $i,X1 : $i,X2 : $i] : (? [X3 : $i] : (($true != (subset @ (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X1 @ X2)))) & ((in @ X3 @ X2) = $true)) & ((in @ X0 @ X1) = $true)) => (? [X3 : $i] : (((subset @ (setadjoin @ (setadjoin @ sK125 @ emptyset) @ (setadjoin @ (setadjoin @ sK125 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ sK126 @ sK127))) != $true) & ((in @ X3 @ sK127) = $true)) & ((in @ sK125 @ sK126) = $true))),
% 78.40/12.31 introduced(definition,[],[choice_axiom])).
% 78.40/12.31 thf(f833,plain,(
% 78.40/12.31 ? [X3 : $i] : (((subset @ (setadjoin @ (setadjoin @ sK125 @ emptyset) @ (setadjoin @ (setadjoin @ sK125 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ sK126 @ sK127))) != $true) & ((in @ X3 @ sK127) = $true)) => (($true != (subset @ (setadjoin @ (setadjoin @ sK125 @ emptyset) @ (setadjoin @ (setadjoin @ sK125 @ (setadjoin @ sK128 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ sK126 @ sK127)))) & ((in @ sK128 @ sK127) = $true))),
% 78.40/12.31 introduced(definition,[],[choice_axiom])).
% 78.40/12.31 thf(f587,plain,(
% 78.40/12.31 (subsetRefl = $true) & (symdiffIneg1 = $true) & (exuI3 = $true) & (subPowSU = $true) & (symdiffI1 = $true) & (setminusER = $true) & (setoftrueEq = $true) & (dsetconstrER = $true) & (binunionE = $true) & (nonemptyE1 = $true) & (nonemptyI = $true) & (uniqinunit = $true) & (setadjoinOr = $true) & (disjointsetsI1 = $true) & (binunionIR = $true) & (subsetE = $true) & (setminusIRneg = $true) & (exuI1 = $true) & (inCongP = $true) & (singletonsswitch = $true) & (emptyInPowerset = $true) & (foundationAx = $true) & (setadjoinIL = $true) & (wellorderingAx = $true) & (powersetsubset = $true) & (subset2powerset = $true) & (descrp = $true) & (emptysetimpfalse = $true) & (upairset2IR = $true) & (binintersectEL = $true) & (setminusI = $true) & (subsetE2 = $true) & (subsetI2 = $true) & (notequalI2 = $true) & (in__Cong = $true) & (setukpairIR = $true) & (singletoninpowerset = $true) & (kpairiskpair = $true) & (notsubsetI = $true) & (exuI2 = $true) & (exuE3e = $true) & (notinemptyset = $true) & (upairsubunion = $true) & (setunionAx = $true) & (subsetTrans = $true) & (setminusILneg = $true) & (binintersectRsub = $true) & (powersetAx = $true) & (emptyI = $true) & (quantDeMorgan2 = $true) & (omega0Ax = $true) & (upairinpowunion = $true) & (replAx = $true) & (emptysetE = $true) & (binintersectSubset1 = $true) & (omegaIndAx = $true) & (binunionRsub = $true) & (binintersectI = $true) & (prop2setE = $true) & (symdiffE = $true) & (powersetE = $true) & (setadjoinIR = $true) & (nonemptyI1 = $true) & (eqimpsubset1 = $true) & (subsetI1 = $true) & (setminusLsub = $true) & (eqimpsubset2 = $true) & (setminusSubset2 = $true) & (setunionE = $true) & (setadjoinE = $true) & (emptysetAx = $true) & (emptyinPowerset = $true) & (exuEu = $true) & (singletoninpowunion = $true) & (notinsingleton = $true) & (setunion__Cong = $true) & (subsetemptysetimpeq = $true) & (descr__Cong = $true) & (upairsetE = $true) & (prop2set2propI = $true) & (binintersectSubset5 = $true) & (setunionI = $true) & (binunionIL = $true) & (setadjoinSub2 = $true) & (powerset__Cong = $true) & (binintersectER = $true) & (prop2setI = $true) & (upairset2E = $true) & (exuE3u = $true) & (notequalI1 = $true) & (exuE1 = $true) & (setminusERneg = $true) & (setadjoinSub = $true) & (quantDeMorgan3 = $true) & (upairsetIL = $true) & (binunionEcases = $true) & (emptysetsubset = $true) & (binintersectLsub = $true) & (kpairp = $true) & (quantDeMorgan1 = $true) & (powersetE1 = $true) & (vacuousDall = $true) & (dsetconstrEL = $true) & (omega__Cong = $true) & (noeltsimpempty = $true) & (setminusEL = $true) & (setminusSubset1 = $true) & (setadjoinAx = $true) & (emptyset__Cong = $true) & (inPowerset = $true) & (omegaSAx = $true) & (dsetconstr__Cong = $true) & (emptyinunitempty = $true) & (sepInPowerset = $true) & (powersetI1 = $true) & (bs114d = $true) & (binintersectSubset2 = $true) & (setukpairIL = $true) & (setextsub = $true) & (setext = $true) & (setadjoin__Cong = $true) & (symdiffIneg2 = $true) & (powersetI = $true) & (symdiffI2 = $true) & (singletonsubset = $true) & (binintersectSubset3 = $true) & (quantDeMorgan4 = $true) & (nonemptyImpWitness = $true) & (setextAx = $true) & (setminusELneg = $true) & (dsetconstrI = $true) & (notdexE = $true) & (upairsetIR = $true) & (setbeta = $true) & (eqinunit = $true) & (emptyE1 = $true) & (exuE2 = $true) & (sepSubset = $true) & (exu__Cong = $true) & (notdallE = $true) & ? [X0 : $i,X1 : $i,X2 : $i] : (? [X3 : $i] : (($true != (subset @ (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X1 @ X2)))) & ((in @ X3 @ X2) = $true)) & ((in @ X0 @ X1) = $true)) & (binunionLsub = $true) & (secondinupair = $true) & (binintersectSubset4 = $true)),
% 78.40/12.31 inference(flattening,[status(thm)],[f586])).
% 78.40/12.31 thf(f586,plain,(
% 78.40/12.31 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((? [X0 : $i,X1 : $i,X2 : $i] : (? [X3 : $i] : (($true != (subset @ (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X1 @ X2)))) & ((in @ X3 @ X2) = $true)) & ((in @ X0 @ X1) = $true)) & (upairinpowunion = $true)) & (upairsubunion = $true)) & (upairset2E = $true)) & (singletoninpowunion = $true)) & (singletoninpowerset = $true)) & (singletonsubset = $true)) & (kpairp = $true)) & (kpairiskpair = $true)) & (setukpairIR = $true)) & (setukpairIL = $true)) & (secondinupair = $true)) & (symdiffIneg2 = $true)) & (symdiffIneg1 = $true)) & (symdiffI2 = $true)) & (symdiffI1 = $true)) & (symdiffE = $true)) & (setminusSubset1 = $true)) & (setminusLsub = $true)) & (setminusIRneg = $true)) & (setminusILneg = $true)) & (setminusELneg = $true)) & (setminusERneg = $true)) & (setminusSubset2 = $true)) & (setminusER = $true)) & (setminusEL = $true)) & (setminusI = $true)) & (bs114d = $true)) & (binintersectSubset1 = $true)) & (binintersectSubset4 = $true)) & (binintersectRsub = $true)) & (disjointsetsI1 = $true)) & (binintersectER = $true)) & (binintersectSubset3 = $true)) & (binintersectSubset2 = $true)) & (binintersectLsub = $true)) & (binintersectEL = $true)) & (binintersectSubset5 = $true)) & (binintersectI = $true)) & (binunionRsub = $true)) & (binunionLsub = $true)) & (binunionE = $true)) & (binunionEcases = $true)) & (binunionIR = $true)) & (upairset2IR = $true)) & (binunionIL = $true)) & (sepSubset = $true)) & (sepInPowerset = $true)) & (powersetsubset = $true)) & (inPowerset = $true)) & (powersetE1 = $true)) & (powersetI1 = $true)) & (subsetemptysetimpeq = $true)) & (setextsub = $true)) & (subset2powerset = $true)) & (setadjoinSub2 = $true)) & (setadjoinSub = $true)) & (subsetTrans = $true)) & (subsetRefl = $true)) & (notequalI2 = $true)) & (notequalI1 = $true)) & (notsubsetI = $true)) & (subsetE2 = $true)) & (subsetE = $true)) & (emptysetsubset = $true)) & (subsetI2 = $true)) & (eqimpsubset1 = $true)) & (eqimpsubset2 = $true)) & (subsetI1 = $true)) & (dsetconstr__Cong = $true)) & (descr__Cong = $true)) & (exuEu = $true)) & (omega__Cong = $true)) & (setunion__Cong = $true)) & (powerset__Cong = $true)) & (setadjoin__Cong = $true)) & (emptyset__Cong = $true)) & (exu__Cong = $true)) & (exuE3u = $true)) & (in__Cong = $true)) & (inCongP = $true)) & (exuI2 = $true)) & (exuI3 = $true)) & (exuI1 = $true)) & (notdallE = $true)) & (notdexE = $true)) & (prop2set2propI = $true)) & (prop2setI = $true)) & (quantDeMorgan4 = $true)) & (quantDeMorgan3 = $true)) & (quantDeMorgan2 = $true)) & (quantDeMorgan1 = $true)) & (vacuousDall = $true)) & (emptyE1 = $true)) & (upairsetIR = $true)) & (upairsetIL = $true)) & (upairsetE = $true)) & (singletonsswitch = $true)) & (eqinunit = $true)) & (notinsingleton = $true)) & (uniqinunit = $true)) & (nonemptyImpWitness = $true)) & (exuE2 = $true)) & (subPowSU = $true)) & (setunionE = $true)) & (setunionI = $true)) & (powersetE = $true)) & (emptyInPowerset = $true)) & (emptyinPowerset = $true)) & (powersetI = $true)) & (setoftrueEq = $true)) & (setadjoinOr = $true)) & (setadjoinE = $true)) & (setadjoinIR = $true)) & (emptyinunitempty = $true)) & (setadjoinIL = $true)) & (nonemptyI1 = $true)) & (nonemptyI = $true)) & (nonemptyE1 = $true)) & (setbeta = $true)) & (noeltsimpempty = $true)) & (emptyI = $true)) & (setext = $true)) & (exuE3e = $true)) & (notinemptyset = $true)) & (emptysetimpfalse = $true)) & (emptysetE = $true)) & (prop2setE = $true)) & (exuE1 = $true)) & (dsetconstrER = $true)) & (dsetconstrEL = $true)) & (dsetconstrI = $true)) & (descrp = $true)) & (wellorderingAx = $true)) & (foundationAx = $true)) & (replAx = $true)) & (omegaIndAx = $true)) & (omegaSAx = $true)) & (omega0Ax = $true)) & (setunionAx = $true)) & (powersetAx = $true)) & (setadjoinAx = $true)) & (emptysetAx = $true)) & (setextAx = $true)),
% 78.40/12.31 inference(ennf_transformation,[status(thm)],[f252])).
% 78.40/12.31 thf(f252,plain,(
% 78.40/12.31 ~((setextAx = $true) => ((emptysetAx = $true) => ((setadjoinAx = $true) => ((powersetAx = $true) => ((setunionAx = $true) => ((omega0Ax = $true) => ((omegaSAx = $true) => ((omegaIndAx = $true) => ((replAx = $true) => ((foundationAx = $true) => ((wellorderingAx = $true) => ((descrp = $true) => ((dsetconstrI = $true) => ((dsetconstrEL = $true) => ((dsetconstrER = $true) => ((exuE1 = $true) => ((prop2setE = $true) => ((emptysetE = $true) => ((emptysetimpfalse = $true) => ((notinemptyset = $true) => ((exuE3e = $true) => ((setext = $true) => ((emptyI = $true) => ((noeltsimpempty = $true) => ((setbeta = $true) => ((nonemptyE1 = $true) => ((nonemptyI = $true) => ((nonemptyI1 = $true) => ((setadjoinIL = $true) => ((emptyinunitempty = $true) => ((setadjoinIR = $true) => ((setadjoinE = $true) => ((setadjoinOr = $true) => ((setoftrueEq = $true) => ((powersetI = $true) => ((emptyinPowerset = $true) => ((emptyInPowerset = $true) => ((powersetE = $true) => ((setunionI = $true) => ((setunionE = $true) => ((subPowSU = $true) => ((exuE2 = $true) => ((nonemptyImpWitness = $true) => ((uniqinunit = $true) => ((notinsingleton = $true) => ((eqinunit = $true) => ((singletonsswitch = $true) => ((upairsetE = $true) => ((upairsetIL = $true) => ((upairsetIR = $true) => ((emptyE1 = $true) => ((vacuousDall = $true) => ((quantDeMorgan1 = $true) => ((quantDeMorgan2 = $true) => ((quantDeMorgan3 = $true) => ((quantDeMorgan4 = $true) => ((prop2setI = $true) => ((prop2set2propI = $true) => ((notdexE = $true) => ((notdallE = $true) => ((exuI1 = $true) => ((exuI3 = $true) => ((exuI2 = $true) => ((inCongP = $true) => ((in__Cong = $true) => ((exuE3u = $true) => ((exu__Cong = $true) => ((emptyset__Cong = $true) => ((setadjoin__Cong = $true) => ((powerset__Cong = $true) => ((setunion__Cong = $true) => ((omega__Cong = $true) => ((exuEu = $true) => ((descr__Cong = $true) => ((dsetconstr__Cong = $true) => ((subsetI1 = $true) => ((eqimpsubset2 = $true) => ((eqimpsubset1 = $true) => ((subsetI2 = $true) => ((emptysetsubset = $true) => ((subsetE = $true) => ((subsetE2 = $true) => ((notsubsetI = $true) => ((notequalI1 = $true) => ((notequalI2 = $true) => ((subsetRefl = $true) => ((subsetTrans = $true) => ((setadjoinSub = $true) => ((setadjoinSub2 = $true) => ((subset2powerset = $true) => ((setextsub = $true) => ((subsetemptysetimpeq = $true) => ((powersetI1 = $true) => ((powersetE1 = $true) => ((inPowerset = $true) => ((powersetsubset = $true) => ((sepInPowerset = $true) => ((sepSubset = $true) => ((binunionIL = $true) => ((upairset2IR = $true) => ((binunionIR = $true) => ((binunionEcases = $true) => ((binunionE = $true) => ((binunionLsub = $true) => ((binunionRsub = $true) => ((binintersectI = $true) => ((binintersectSubset5 = $true) => ((binintersectEL = $true) => ((binintersectLsub = $true) => ((binintersectSubset2 = $true) => ((binintersectSubset3 = $true) => ((binintersectER = $true) => ((disjointsetsI1 = $true) => ((binintersectRsub = $true) => ((binintersectSubset4 = $true) => ((binintersectSubset1 = $true) => ((bs114d = $true) => ((setminusI = $true) => ((setminusEL = $true) => ((setminusER = $true) => ((setminusSubset2 = $true) => ((setminusERneg = $true) => ((setminusELneg = $true) => ((setminusILneg = $true) => ((setminusIRneg = $true) => ((setminusLsub = $true) => ((setminusSubset1 = $true) => ((symdiffE = $true) => ((symdiffI1 = $true) => ((symdiffI2 = $true) => ((symdiffIneg1 = $true) => ((symdiffIneg2 = $true) => ((secondinupair = $true) => ((setukpairIL = $true) => ((setukpairIR = $true) => ((kpairiskpair = $true) => ((kpairp = $true) => ((singletonsubset = $true) => ((singletoninpowerset = $true) => ((singletoninpowunion = $true) => ((upairset2E = $true) => ((upairsubunion = $true) => ((upairinpowunion = $true) => ! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X0 @ X1) = $true) => ! [X3 : $i] : (((in @ X3 @ X2) = $true) => ($true = (subset @ (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X1 @ X2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 78.40/12.31 inference(fool_elimination,[status(thm)],[f251])).
% 78.40/12.31 thf(f251,plain,(
% 78.40/12.31 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ X1) => ! [X3 : $i] : ((in @ X3 @ X2) => (subset @ (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X1 @ X2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 78.40/12.31 inference(rectify,[status(thm)],[f150])).
% 78.40/12.31 thf(f150,negated_conjecture,(
% 78.40/12.31 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => ! [X1 : $i,X3 : $i,X4 : $i] : ((in @ X1 @ X3) => ! [X2 : $i] : ((in @ X2 @ X4) => (subset @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X3 @ X4))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 78.40/12.31 inference(negated_conjecture,[status(cth)],[f149])).
% 78.40/12.31 thf(f149,conjecture,(
% 78.40/12.31 setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => ! [X1 : $i,X3 : $i,X4 : $i] : ((in @ X1 @ X3) => ! [X2 : $i] : ((in @ X2 @ X4) => (subset @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X3 @ X4)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 78.40/12.31 file('/export/starexec/sandbox/tmp/tmp.EC9PjZGDVh/DTF2THF_12319.p',ubforcartprodlem1)).
% 78.40/12.31 thf(f9109,plain,(
% 78.40/12.31 (upairsubunion != $true) | ~spl395_14),
% 78.40/12.31 inference(subsumption_resolution,[status(thm)],[f9108,f1467])).
% 78.40/12.31 thf(f1467,plain,(
% 78.40/12.31 ((in @ sK128 @ sK127) = $true)),
% 78.40/12.31 inference(cnf_transformation,[status(thm)],[f834])).
% 78.40/12.31 thf(f9108,plain,(
% 78.40/12.31 ((in @ sK128 @ sK127) != $true) | (upairsubunion != $true) | ~spl395_14),
% 78.40/12.31 inference(subsumption_resolution,[status(thm)],[f9101,f1466])).
% 78.40/12.31 thf(f1466,plain,(
% 78.40/12.31 ((in @ sK125 @ sK126) = $true)),
% 78.40/12.31 inference(cnf_transformation,[status(thm)],[f834])).
% 78.40/12.31 thf(f9101,plain,(
% 78.40/12.31 ((in @ sK125 @ sK126) != $true) | ((in @ sK128 @ sK127) != $true) | (upairsubunion != $true) | ~spl395_14),
% 78.40/12.31 inference(trivial_inequality_removal,[status(thm)],[f9095])).
% 78.40/12.31 thf(f9095,plain,(
% 78.40/12.31 (upairsubunion != $true) | ((in @ sK125 @ sK126) != $true) | ($true != $true) | ((in @ sK128 @ sK127) != $true) | ~spl395_14),
% 78.40/12.31 inference(superposition,[status(thm)],[f9091,f1339])).
% 78.40/12.31 thf(f1339,plain,(
% 78.40/12.31 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((subset @ (setadjoin @ X1 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X2 @ X0)) = $true) | ((in @ X3 @ X0) != $true) | ((in @ X1 @ X2) != $true) | (upairsubunion != $true)) )),
% 78.40/12.31 inference(cnf_transformation,[status(thm)],[f687])).
% 78.40/12.31 thf(f687,plain,(
% 78.40/12.31 (! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X1 @ X2) != $true) | ! [X3 : $i] : (((subset @ (setadjoin @ X1 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X2 @ X0)) = $true) | ((in @ X3 @ X0) != $true))) | (upairsubunion != $true)) & ((upairsubunion = $true) | (($true = (in @ sK34 @ sK35)) & (($true != (subset @ (setadjoin @ sK34 @ (setadjoin @ sK36 @ emptyset)) @ (binunion @ sK35 @ sK33))) & ((in @ sK36 @ sK33) = $true))))),
% 78.40/12.31 inference(skolemisation,[status(esa),new_symbols(skolem,[sK33,sK34,sK35,sK36])],[f684,f686,f685])).
% 78.40/12.31 thf(f685,plain,(
% 78.40/12.31 ? [X4 : $i,X5 : $i,X6 : $i] : (((in @ X5 @ X6) = $true) & ? [X7 : $i] : (((subset @ (setadjoin @ X5 @ (setadjoin @ X7 @ emptyset)) @ (binunion @ X6 @ X4)) != $true) & ((in @ X7 @ X4) = $true))) => (($true = (in @ sK34 @ sK35)) & ? [X7 : $i] : (((subset @ (setadjoin @ sK34 @ (setadjoin @ X7 @ emptyset)) @ (binunion @ sK35 @ sK33)) != $true) & ((in @ X7 @ sK33) = $true)))),
% 78.40/12.31 introduced(definition,[],[choice_axiom])).
% 78.40/12.31 thf(f686,plain,(
% 78.40/12.31 ? [X7 : $i] : (((subset @ (setadjoin @ sK34 @ (setadjoin @ X7 @ emptyset)) @ (binunion @ sK35 @ sK33)) != $true) & ((in @ X7 @ sK33) = $true)) => (($true != (subset @ (setadjoin @ sK34 @ (setadjoin @ sK36 @ emptyset)) @ (binunion @ sK35 @ sK33))) & ((in @ sK36 @ sK33) = $true))),
% 78.40/12.31 introduced(definition,[],[choice_axiom])).
% 78.40/12.31 thf(f684,plain,(
% 78.40/12.31 (! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X1 @ X2) != $true) | ! [X3 : $i] : (((subset @ (setadjoin @ X1 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X2 @ X0)) = $true) | ((in @ X3 @ X0) != $true))) | (upairsubunion != $true)) & ((upairsubunion = $true) | ? [X4 : $i,X5 : $i,X6 : $i] : (((in @ X5 @ X6) = $true) & ? [X7 : $i] : (((subset @ (setadjoin @ X5 @ (setadjoin @ X7 @ emptyset)) @ (binunion @ X6 @ X4)) != $true) & ((in @ X7 @ X4) = $true))))),
% 78.40/12.31 inference(rectify,[status(thm)],[f683])).
% 78.40/12.31 thf(f683,plain,(
% 78.40/12.31 (! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X1 @ X2) != $true) | ! [X3 : $i] : (((subset @ (setadjoin @ X1 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X2 @ X0)) = $true) | ((in @ X3 @ X0) != $true))) | (upairsubunion != $true)) & ((upairsubunion = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X1 @ X2) = $true) & ? [X3 : $i] : (((subset @ (setadjoin @ X1 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X2 @ X0)) != $true) & ((in @ X3 @ X0) = $true))))),
% 78.40/12.31 inference(nnf_transformation,[status(thm)],[f621])).
% 78.40/12.31 thf(f621,plain,(
% 78.40/12.31 ! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X1 @ X2) != $true) | ! [X3 : $i] : (((subset @ (setadjoin @ X1 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X2 @ X0)) = $true) | ((in @ X3 @ X0) != $true))) <=> (upairsubunion = $true)),
% 78.40/12.31 inference(ennf_transformation,[status(thm)],[f248])).
% 78.40/12.31 thf(f248,plain,(
% 78.40/12.31 (upairsubunion = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X1 @ X2) = $true) => ! [X3 : $i] : (((in @ X3 @ X0) = $true) => ((subset @ (setadjoin @ X1 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X2 @ X0)) = $true)))),
% 78.40/12.31 inference(fool_elimination,[status(thm)],[f247])).
% 78.40/12.31 thf(f247,plain,(
% 78.40/12.31 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ X2) => ! [X3 : $i] : ((in @ X3 @ X0) => (subset @ (setadjoin @ X1 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X2 @ X0)))) = upairsubunion)),
% 78.40/12.31 inference(rectify,[status(thm)],[f147])).
% 78.40/12.31 thf(f147,axiom,(
% 78.40/12.31 (! [X4 : $i,X1 : $i,X3 : $i] : ((in @ X1 @ X3) => ! [X2 : $i] : ((in @ X2 @ X4) => (subset @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ (binunion @ X3 @ X4)))) = upairsubunion)),
% 78.40/12.31 file('/export/starexec/sandbox/tmp/tmp.EC9PjZGDVh/DTF2THF_12319.p',upairsubunion)).
% 78.40/12.31 thf(f9091,plain,(
% 78.40/12.31 ($true != (subset @ (setadjoin @ sK125 @ (setadjoin @ sK128 @ emptyset)) @ (binunion @ sK126 @ sK127))) | ~spl395_14),
% 78.40/12.31 inference(subsumption_resolution,[status(thm)],[f9088,f1584])).
% 78.40/12.31 thf(f1584,plain,(
% 78.40/12.31 (powersetsubset = $true)),
% 78.40/12.31 inference(cnf_transformation,[status(thm)],[f834])).
% 78.40/12.31 thf(f9088,plain,(
% 78.40/12.31 (powersetsubset != $true) | ($true != (subset @ (setadjoin @ sK125 @ (setadjoin @ sK128 @ emptyset)) @ (binunion @ sK126 @ sK127))) | ~spl395_14),
% 78.40/12.31 inference(trivial_inequality_removal,[status(thm)],[f9080])).
% 78.40/12.31 thf(f9080,plain,(
% 78.40/12.31 (powersetsubset != $true) | ($true != $true) | ($true != (subset @ (setadjoin @ sK125 @ (setadjoin @ sK128 @ emptyset)) @ (binunion @ sK126 @ sK127))) | ~spl395_14),
% 78.40/12.31 inference(superposition,[status(thm)],[f9073,f1688])).
% 78.40/12.31 thf(f1688,plain,(
% 78.40/12.31 ( ! [X0 : $i,X1 : $i] : (((subset @ (powerset @ X0) @ (powerset @ X1)) = $true) | (powersetsubset != $true) | ((subset @ X0 @ X1) != $true)) )),
% 78.40/12.31 inference(cnf_transformation,[status(thm)],[f934])).
% 78.40/12.31 thf(f934,plain,(
% 78.40/12.31 (! [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) != $true) | ((subset @ (powerset @ X0) @ (powerset @ X1)) = $true)) | (powersetsubset != $true)) & ((powersetsubset = $true) | (((subset @ sK187 @ sK188) = $true) & ((subset @ (powerset @ sK187) @ (powerset @ sK188)) != $true)))),
% 78.40/12.31 inference(skolemisation,[status(esa),new_symbols(skolem,[sK187,sK188])],[f932,f933])).
% 78.40/12.31 thf(f933,plain,(
% 78.40/12.31 ? [X2 : $i,X3 : $i] : (($true = (subset @ X2 @ X3)) & ((subset @ (powerset @ X2) @ (powerset @ X3)) != $true)) => (((subset @ sK187 @ sK188) = $true) & ((subset @ (powerset @ sK187) @ (powerset @ sK188)) != $true))),
% 78.40/12.31 introduced(definition,[],[choice_axiom])).
% 78.40/12.31 thf(f932,plain,(
% 78.40/12.31 (! [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) != $true) | ((subset @ (powerset @ X0) @ (powerset @ X1)) = $true)) | (powersetsubset != $true)) & ((powersetsubset = $true) | ? [X2 : $i,X3 : $i] : (($true = (subset @ X2 @ X3)) & ((subset @ (powerset @ X2) @ (powerset @ X3)) != $true)))),
% 78.40/12.31 inference(rectify,[status(thm)],[f931])).
% 78.40/12.31 thf(f931,plain,(
% 78.40/12.31 (! [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) != $true) | ((subset @ (powerset @ X0) @ (powerset @ X1)) = $true)) | (powersetsubset != $true)) & ((powersetsubset = $true) | ? [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) = $true) & ((subset @ (powerset @ X0) @ (powerset @ X1)) != $true)))),
% 78.40/12.31 inference(nnf_transformation,[status(thm)],[f583])).
% 78.40/12.31 thf(f583,plain,(
% 78.40/12.31 ! [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) != $true) | ((subset @ (powerset @ X0) @ (powerset @ X1)) = $true)) <=> (powersetsubset = $true)),
% 78.40/12.31 inference(ennf_transformation,[status(thm)],[f329])).
% 78.40/12.31 thf(f329,plain,(
% 78.40/12.31 (powersetsubset = $true) <=> ! [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) = $true) => ((subset @ (powerset @ X0) @ (powerset @ X1)) = $true))),
% 78.40/12.31 inference(fool_elimination,[status(thm)],[f328])).
% 78.40/12.31 thf(f328,plain,(
% 78.40/12.31 (! [X0 : $i,X1 : $i] : ((subset @ X0 @ X1) => (subset @ (powerset @ X0) @ (powerset @ X1))) = powersetsubset)),
% 78.40/12.31 inference(rectify,[status(thm)],[f98])).
% 78.40/12.31 thf(f98,axiom,(
% 78.40/12.31 (! [X3 : $i,X4 : $i] : ((subset @ X3 @ X4) => (subset @ (powerset @ X3) @ (powerset @ X4))) = powersetsubset)),
% 78.40/12.31 file('/export/starexec/sandbox/tmp/tmp.EC9PjZGDVh/DTF2THF_12319.p',powersetsubset)).
% 78.40/12.31 thf(f9073,plain,(
% 78.40/12.31 ((subset @ (powerset @ (setadjoin @ sK125 @ (setadjoin @ sK128 @ emptyset))) @ (powerset @ (binunion @ sK126 @ sK127))) != $true) | ~spl395_14),
% 78.40/12.31 inference(subsumption_resolution,[status(thm)],[f9007,f1499])).
% 78.40/12.31 thf(f1499,plain,(
% 78.40/12.31 (inPowerset = $true)),
% 78.40/12.31 inference(cnf_transformation,[status(thm)],[f834])).
% 78.40/12.31 thf(f9007,plain,(
% 78.40/12.31 (inPowerset != $true) | ((subset @ (powerset @ (setadjoin @ sK125 @ (setadjoin @ sK128 @ emptyset))) @ (powerset @ (binunion @ sK126 @ sK127))) != $true) | ~spl395_14),
% 78.40/12.31 inference(trivial_inequality_removal,[status(thm)],[f8973])).
% 78.40/12.31 thf(f8973,plain,(
% 78.40/12.31 ($true != $true) | (inPowerset != $true) | ((subset @ (powerset @ (setadjoin @ sK125 @ (setadjoin @ sK128 @ emptyset))) @ (powerset @ (binunion @ sK126 @ sK127))) != $true) | ~spl395_14),
% 78.40/12.31 inference(superposition,[status(thm)],[f8939,f1771])).
% 78.40/12.31 thf(f1771,plain,(
% 78.40/12.31 ( ! [X1 : $i] : (((in @ X1 @ (powerset @ X1)) = $true) | (inPowerset != $true)) )),
% 78.40/12.31 inference(cnf_transformation,[status(thm)],[f1025])).
% 78.40/12.31 thf(f1025,plain,(
% 78.40/12.31 ((inPowerset = $true) | ((in @ sK239 @ (powerset @ sK239)) != $true)) & (! [X1 : $i] : ((in @ X1 @ (powerset @ X1)) = $true) | (inPowerset != $true))),
% 78.40/12.31 inference(skolemisation,[status(esa),new_symbols(skolem,[sK239])],[f1023,f1024])).
% 78.40/12.31 thf(f1024,plain,(
% 78.40/12.31 ? [X0 : $i] : ((in @ X0 @ (powerset @ X0)) != $true) => ((in @ sK239 @ (powerset @ sK239)) != $true)),
% 78.40/12.31 introduced(definition,[],[choice_axiom])).
% 78.40/12.31 thf(f1023,plain,(
% 78.40/12.31 ((inPowerset = $true) | ? [X0 : $i] : ((in @ X0 @ (powerset @ X0)) != $true)) & (! [X1 : $i] : ((in @ X1 @ (powerset @ X1)) = $true) | (inPowerset != $true))),
% 78.40/12.31 inference(rectify,[status(thm)],[f1022])).
% 78.40/12.31 thf(f1022,plain,(
% 78.40/12.31 ((inPowerset = $true) | ? [X0 : $i] : ((in @ X0 @ (powerset @ X0)) != $true)) & (! [X0 : $i] : ((in @ X0 @ (powerset @ X0)) = $true) | (inPowerset != $true))),
% 78.40/12.31 inference(nnf_transformation,[status(thm)],[f202])).
% 78.40/12.31 thf(f202,plain,(
% 78.40/12.31 (inPowerset = $true) <=> ! [X0 : $i] : ((in @ X0 @ (powerset @ X0)) = $true)),
% 78.40/12.31 inference(fool_elimination,[status(thm)],[f201])).
% 78.40/12.31 thf(f201,plain,(
% 78.40/12.31 (! [X0 : $i] : (in @ X0 @ (powerset @ X0)) = inPowerset)),
% 78.40/12.31 inference(rectify,[status(thm)],[f97])).
% 78.40/12.31 thf(f97,axiom,(
% 78.40/12.31 (! [X3 : $i] : (in @ X3 @ (powerset @ X3)) = inPowerset)),
% 78.40/12.31 file('/export/starexec/sandbox/tmp/tmp.EC9PjZGDVh/DTF2THF_12319.p',inPowerset)).
% 78.40/12.31 thf(f8939,plain,(
% 78.40/12.31 ( ! [X0 : $i] : (($true != (in @ (setadjoin @ sK125 @ (setadjoin @ sK128 @ emptyset)) @ X0)) | ((subset @ X0 @ (powerset @ (binunion @ sK126 @ sK127))) != $true)) ) | ~spl395_14),
% 78.40/12.31 inference(subsumption_resolution,[status(thm)],[f8925,f1463])).
% 78.40/12.31 thf(f1463,plain,(
% 78.40/12.31 (binintersectSubset4 = $true)),
% 78.40/12.31 inference(cnf_transformation,[status(thm)],[f834])).
% 78.40/12.31 thf(f8925,plain,(
% 78.40/12.31 ( ! [X0 : $i] : (((subset @ X0 @ (powerset @ (binunion @ sK126 @ sK127))) != $true) | (binintersectSubset4 != $true) | ($true != (in @ (setadjoin @ sK125 @ (setadjoin @ sK128 @ emptyset)) @ X0))) ) | ~spl395_14),
% 78.40/12.31 inference(superposition,[status(thm)],[f8592,f1841])).
% 78.40/12.31 thf(f1841,plain,(
% 78.40/12.31 ( ! [X2 : $i,X3 : $i] : (((binintersect @ X2 @ X3) = X3) | (binintersectSubset4 != $true) | ((subset @ X3 @ X2) != $true)) )),
% 78.40/12.31 inference(cnf_transformation,[status(thm)],[f1111])).
% 78.40/12.31 thf(f1111,plain,(
% 78.40/12.31 ((binintersectSubset4 = $true) | ((sK288 != (binintersect @ sK287 @ sK288)) & ((subset @ sK288 @ sK287) = $true))) & (! [X2 : $i,X3 : $i] : (((binintersect @ X2 @ X3) = X3) | ((subset @ X3 @ X2) != $true)) | (binintersectSubset4 != $true))),
% 78.40/12.31 inference(skolemisation,[status(esa),new_symbols(skolem,[sK287,sK288])],[f1109,f1110])).
% 78.40/12.31 thf(f1110,plain,(
% 78.40/12.31 ? [X0 : $i,X1 : $i] : (((binintersect @ X0 @ X1) != X1) & ((subset @ X1 @ X0) = $true)) => ((sK288 != (binintersect @ sK287 @ sK288)) & ((subset @ sK288 @ sK287) = $true))),
% 78.40/12.31 introduced(definition,[],[choice_axiom])).
% 78.40/12.31 thf(f1109,plain,(
% 78.40/12.31 ((binintersectSubset4 = $true) | ? [X0 : $i,X1 : $i] : (((binintersect @ X0 @ X1) != X1) & ((subset @ X1 @ X0) = $true))) & (! [X2 : $i,X3 : $i] : (((binintersect @ X2 @ X3) = X3) | ((subset @ X3 @ X2) != $true)) | (binintersectSubset4 != $true))),
% 78.40/12.31 inference(rectify,[status(thm)],[f1108])).
% 78.40/12.31 thf(f1108,plain,(
% 78.40/12.31 ((binintersectSubset4 = $true) | ? [X0 : $i,X1 : $i] : (((binintersect @ X0 @ X1) != X1) & ((subset @ X1 @ X0) = $true))) & (! [X0 : $i,X1 : $i] : (((binintersect @ X0 @ X1) = X1) | ((subset @ X1 @ X0) != $true)) | (binintersectSubset4 != $true))),
% 78.40/12.31 inference(nnf_transformation,[status(thm)],[f502])).
% 78.40/12.31 thf(f502,plain,(
% 78.40/12.31 (binintersectSubset4 = $true) <=> ! [X0 : $i,X1 : $i] : (((binintersect @ X0 @ X1) = X1) | ((subset @ X1 @ X0) != $true))),
% 78.40/12.31 inference(ennf_transformation,[status(thm)],[f220])).
% 78.40/12.31 thf(f220,plain,(
% 78.40/12.31 ! [X0 : $i,X1 : $i] : (((subset @ X1 @ X0) = $true) => ((binintersect @ X0 @ X1) = X1)) <=> (binintersectSubset4 = $true)),
% 78.40/12.31 inference(fool_elimination,[status(thm)],[f219])).
% 78.40/12.31 thf(f219,plain,(
% 78.40/12.31 (binintersectSubset4 = ! [X0 : $i,X1 : $i] : ((subset @ X1 @ X0) => ((binintersect @ X0 @ X1) = X1)))),
% 78.40/12.31 inference(rectify,[status(thm)],[f117])).
% 78.40/12.31 thf(f117,axiom,(
% 78.40/12.31 (binintersectSubset4 = ! [X3 : $i,X4 : $i] : ((subset @ X4 @ X3) => ((binintersect @ X3 @ X4) = X4)))),
% 78.40/12.31 file('/export/starexec/sandbox/tmp/tmp.EC9PjZGDVh/DTF2THF_12319.p',binintersectSubset4)).
% 78.40/12.31 thf(f8592,plain,(
% 78.40/12.31 ( ! [X1 : $i] : (((in @ (setadjoin @ sK125 @ (setadjoin @ sK128 @ emptyset)) @ (binintersect @ (powerset @ (binunion @ sK126 @ sK127)) @ X1)) != $true)) ) | ~spl395_14),
% 78.40/12.31 inference(avatar_component_clause,[status(thm)],[f8591])).
% 78.40/12.31 thf(f8591,definition,(
% 78.40/12.31 spl395_14 <=> ! [X1 : $i] : ((in @ (setadjoin @ sK125 @ (setadjoin @ sK128 @ emptyset)) @ (binintersect @ (powerset @ (binunion @ sK126 @ sK127)) @ X1)) != $true)),
% 78.40/12.31 introduced(definition,[new_symbols(naming,[spl395_14])],[avatar_definition])).
% 78.40/12.31 thf(f8880,plain,(
% 78.40/12.31 ~spl395_13),
% 78.40/12.31 inference(avatar_contradiction_clause,[status(thm)],[f8879])).
% 78.40/12.31 thf(f8879,plain,(
% 78.40/12.31 $false | ~spl395_13),
% 78.40/12.31 inference(subsumption_resolution,[status(thm)],[f8878,f1466])).
% 78.40/12.31 thf(f8878,plain,(
% 78.40/12.31 ((in @ sK125 @ sK126) != $true) | ~spl395_13),
% 78.40/12.31 inference(subsumption_resolution,[status(thm)],[f8870,f1535])).
% 78.40/12.31 thf(f1535,plain,(
% 78.40/12.31 (singletoninpowunion = $true)),
% 78.40/12.31 inference(cnf_transformation,[status(thm)],[f834])).
% 78.40/12.31 thf(f8870,plain,(
% 78.40/12.31 (singletoninpowunion != $true) | ((in @ sK125 @ sK126) != $true) | ~spl395_13),
% 78.40/12.31 inference(trivial_inequality_removal,[status(thm)],[f8858])).
% 78.40/12.31 thf(f8858,plain,(
% 78.40/12.31 ($true != $true) | ((in @ sK125 @ sK126) != $true) | (singletoninpowunion != $true) | ~spl395_13),
% 78.40/12.31 inference(superposition,[status(thm)],[f8650,f1838])).
% 78.40/12.31 thf(f1838,plain,(
% 78.40/12.31 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ (setadjoin @ X5 @ emptyset) @ (powerset @ (binunion @ X4 @ X3))) = $true) | (singletoninpowunion != $true) | ((in @ X5 @ X4) != $true)) )),
% 78.40/12.31 inference(cnf_transformation,[status(thm)],[f1107])).
% 78.40/12.31 thf(f1107,plain,(
% 78.40/12.31 ((singletoninpowunion = $true) | (((in @ (setadjoin @ sK286 @ emptyset) @ (powerset @ (binunion @ sK285 @ sK284))) != $true) & ((in @ sK286 @ sK285) = $true))) & (! [X3 : $i,X4 : $i,X5 : $i] : (((in @ (setadjoin @ X5 @ emptyset) @ (powerset @ (binunion @ X4 @ X3))) = $true) | ((in @ X5 @ X4) != $true)) | (singletoninpowunion != $true))),
% 78.40/12.31 inference(skolemisation,[status(esa),new_symbols(skolem,[sK284,sK285,sK286])],[f1105,f1106])).
% 78.40/12.31 thf(f1106,plain,(
% 78.40/12.31 ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X1 @ X0))) != $true) & ((in @ X2 @ X1) = $true)) => (((in @ (setadjoin @ sK286 @ emptyset) @ (powerset @ (binunion @ sK285 @ sK284))) != $true) & ((in @ sK286 @ sK285) = $true))),
% 78.40/12.31 introduced(definition,[],[choice_axiom])).
% 78.40/12.31 thf(f1105,plain,(
% 78.40/12.31 ((singletoninpowunion = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X1 @ X0))) != $true) & ((in @ X2 @ X1) = $true))) & (! [X3 : $i,X4 : $i,X5 : $i] : (((in @ (setadjoin @ X5 @ emptyset) @ (powerset @ (binunion @ X4 @ X3))) = $true) | ((in @ X5 @ X4) != $true)) | (singletoninpowunion != $true))),
% 78.40/12.31 inference(rectify,[status(thm)],[f1104])).
% 78.40/12.31 thf(f1104,plain,(
% 78.40/12.31 ((singletoninpowunion = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X1 @ X0))) != $true) & ((in @ X2 @ X1) = $true))) & (! [X0 : $i,X1 : $i,X2 : $i] : (((in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X1 @ X0))) = $true) | ((in @ X2 @ X1) != $true)) | (singletoninpowunion != $true))),
% 78.40/12.31 inference(nnf_transformation,[status(thm)],[f578])).
% 78.40/12.31 thf(f578,plain,(
% 78.40/12.31 (singletoninpowunion = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (((in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X1 @ X0))) = $true) | ((in @ X2 @ X1) != $true))),
% 78.40/12.31 inference(ennf_transformation,[status(thm)],[f269])).
% 78.40/12.31 thf(f269,plain,(
% 78.40/12.31 ! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ X1) = $true) => ((in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X1 @ X0))) = $true)) <=> (singletoninpowunion = $true)),
% 78.40/12.31 inference(fool_elimination,[status(thm)],[f268])).
% 78.40/12.31 thf(f268,plain,(
% 78.40/12.31 (singletoninpowunion = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ X1) => (in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X1 @ X0)))))),
% 78.40/12.31 inference(rectify,[status(thm)],[f145])).
% 78.40/12.31 thf(f145,axiom,(
% 78.40/12.31 (singletoninpowunion = ! [X4 : $i,X3 : $i,X1 : $i] : ((in @ X1 @ X3) => (in @ (setadjoin @ X1 @ emptyset) @ (powerset @ (binunion @ X3 @ X4)))))),
% 78.40/12.31 file('/export/starexec/sandbox/tmp/tmp.EC9PjZGDVh/DTF2THF_12319.p',singletoninpowunion)).
% 78.40/12.31 thf(f8650,plain,(
% 78.40/12.31 ((in @ (setadjoin @ sK125 @ emptyset) @ (powerset @ (binunion @ sK126 @ sK127))) != $true) | ~spl395_13),
% 78.40/12.31 inference(subsumption_resolution,[status(thm)],[f8640,f1542])).
% 78.40/12.31 thf(f1542,plain,(
% 78.40/12.31 (eqimpsubset2 = $true)),
% 78.40/12.31 inference(cnf_transformation,[status(thm)],[f834])).
% 78.40/12.31 thf(f8640,plain,(
% 78.40/12.31 (eqimpsubset2 != $true) | ((in @ (setadjoin @ sK125 @ emptyset) @ (powerset @ (binunion @ sK126 @ sK127))) != $true) | ~spl395_13),
% 78.40/12.31 inference(trivial_inequality_removal,[status(thm)],[f8615])).
% 78.40/12.31 thf(f8615,plain,(
% 78.40/12.31 ($true != $true) | ((in @ (setadjoin @ sK125 @ emptyset) @ (powerset @ (binunion @ sK126 @ sK127))) != $true) | (eqimpsubset2 != $true) | ~spl395_13),
% 78.40/12.31 inference(superposition,[status(thm)],[f8609,f2011])).
% 78.40/12.31 thf(f2011,plain,(
% 78.40/12.31 ( ! [X3 : $i] : (((subset @ X3 @ X3) = $true) | (eqimpsubset2 != $true)) )),
% 78.40/12.31 inference(equality_resolution,[status(thm)],[f1701])).
% 78.40/12.31 thf(f1701,plain,(
% 78.40/12.31 ( ! [X2 : $i,X3 : $i] : ((X2 != X3) | ($true = (subset @ X2 @ X3)) | (eqimpsubset2 != $true)) )),
% 78.40/12.31 inference(cnf_transformation,[status(thm)],[f954])).
% 78.40/12.31 thf(f954,plain,(
% 78.40/12.31 ((eqimpsubset2 = $true) | ((sK200 = sK199) & ((subset @ sK199 @ sK200) != $true))) & (! [X2 : $i,X3 : $i] : ((X2 != X3) | ($true = (subset @ X2 @ X3))) | (eqimpsubset2 != $true))),
% 78.40/12.31 inference(skolemisation,[status(esa),new_symbols(skolem,[sK199,sK200])],[f952,f953])).
% 78.40/12.31 thf(f953,plain,(
% 78.40/12.31 ? [X0 : $i,X1 : $i] : ((X0 = X1) & ((subset @ X0 @ X1) != $true)) => ((sK200 = sK199) & ((subset @ sK199 @ sK200) != $true))),
% 78.40/12.31 introduced(definition,[],[choice_axiom])).
% 78.40/12.31 thf(f952,plain,(
% 78.40/12.31 ((eqimpsubset2 = $true) | ? [X0 : $i,X1 : $i] : ((X0 = X1) & ((subset @ X0 @ X1) != $true))) & (! [X2 : $i,X3 : $i] : ((X2 != X3) | ($true = (subset @ X2 @ X3))) | (eqimpsubset2 != $true))),
% 78.40/12.31 inference(rectify,[status(thm)],[f951])).
% 78.40/12.31 thf(f951,plain,(
% 78.40/12.31 ((eqimpsubset2 = $true) | ? [X0 : $i,X1 : $i] : ((X0 = X1) & ((subset @ X0 @ X1) != $true))) & (! [X0 : $i,X1 : $i] : ((X0 != X1) | ((subset @ X0 @ X1) = $true)) | (eqimpsubset2 != $true))),
% 78.40/12.31 inference(nnf_transformation,[status(thm)],[f512])).
% 78.40/12.31 thf(f512,plain,(
% 78.40/12.31 (eqimpsubset2 = $true) <=> ! [X0 : $i,X1 : $i] : ((X0 != X1) | ((subset @ X0 @ X1) = $true))),
% 78.40/12.31 inference(ennf_transformation,[status(thm)],[f385])).
% 78.40/12.31 thf(f385,plain,(
% 78.40/12.31 (eqimpsubset2 = $true) <=> ! [X0 : $i,X1 : $i] : ((X0 = X1) => ((subset @ X0 @ X1) = $true))),
% 78.40/12.31 inference(fool_elimination,[status(thm)],[f384])).
% 78.40/12.31 thf(f384,plain,(
% 78.40/12.31 (eqimpsubset2 = ! [X0 : $i,X1 : $i] : ((X0 = X1) => (subset @ X0 @ X1)))),
% 78.40/12.31 inference(rectify,[status(thm)],[f79])).
% 78.40/12.31 thf(f79,axiom,(
% 78.40/12.31 (eqimpsubset2 = ! [X4 : $i,X3 : $i] : ((X3 = X4) => (subset @ X4 @ X3)))),
% 78.40/12.31 file('/export/starexec/sandbox/tmp/tmp.EC9PjZGDVh/DTF2THF_12319.p',eqimpsubset2)).
% 78.40/12.31 thf(f8609,plain,(
% 78.40/12.31 ( ! [X0 : $i] : (((subset @ X0 @ (powerset @ (binunion @ sK126 @ sK127))) != $true) | ($true != (in @ (setadjoin @ sK125 @ emptyset) @ X0))) ) | ~spl395_13),
% 78.40/12.31 inference(subsumption_resolution,[status(thm)],[f8594,f1463])).
% 78.40/12.31 thf(f8594,plain,(
% 78.40/12.31 ( ! [X0 : $i] : ((binintersectSubset4 != $true) | ($true != (in @ (setadjoin @ sK125 @ emptyset) @ X0)) | ((subset @ X0 @ (powerset @ (binunion @ sK126 @ sK127))) != $true)) ) | ~spl395_13),
% 78.40/12.31 inference(superposition,[status(thm)],[f8589,f1841])).
% 78.40/12.31 thf(f8589,plain,(
% 78.40/12.31 ( ! [X0 : $i] : (((in @ (setadjoin @ sK125 @ emptyset) @ (binintersect @ (powerset @ (binunion @ sK126 @ sK127)) @ X0)) != $true)) ) | ~spl395_13),
% 78.40/12.31 inference(avatar_component_clause,[status(thm)],[f8588])).
% 78.40/12.31 thf(f8588,definition,(
% 78.40/12.31 spl395_13 <=> ! [X0 : $i] : ((in @ (setadjoin @ sK125 @ emptyset) @ (binintersect @ (powerset @ (binunion @ sK126 @ sK127)) @ X0)) != $true)),
% 78.40/12.31 introduced(definition,[new_symbols(naming,[spl395_13])],[avatar_definition])).
% 78.40/12.31 thf(f8593,plain,(
% 78.40/12.31 spl395_13 | spl395_14),
% 78.40/12.31 inference(avatar_split_clause,[status(thm)],[f8584,f8591,f8588])).
% 78.40/12.31 thf(f8584,plain,(
% 78.40/12.31 ( ! [X0 : $i,X1 : $i] : (((in @ (setadjoin @ sK125 @ (setadjoin @ sK128 @ emptyset)) @ (binintersect @ (powerset @ (binunion @ sK126 @ sK127)) @ X1)) != $true) | ((in @ (setadjoin @ sK125 @ emptyset) @ (binintersect @ (powerset @ (binunion @ sK126 @ sK127)) @ X0)) != $true)) )),
% 78.40/12.31 inference(subsumption_resolution,[status(thm)],[f8581,f1511])).
% 78.40/12.31 thf(f1511,plain,(
% 78.40/12.31 (binintersectLsub = $true)),
% 78.40/12.31 inference(cnf_transformation,[status(thm)],[f834])).
% 78.40/12.31 thf(f8581,plain,(
% 78.40/12.31 ( ! [X0 : $i,X1 : $i] : (((in @ (setadjoin @ sK125 @ emptyset) @ (binintersect @ (powerset @ (binunion @ sK126 @ sK127)) @ X0)) != $true) | ((in @ (setadjoin @ sK125 @ (setadjoin @ sK128 @ emptyset)) @ (binintersect @ (powerset @ (binunion @ sK126 @ sK127)) @ X1)) != $true) | (binintersectLsub != $true)) )),
% 78.40/12.31 inference(trivial_inequality_removal,[status(thm)],[f8572])).
% 78.40/12.31 thf(f8572,plain,(
% 78.40/12.31 ( ! [X0 : $i,X1 : $i] : ((binintersectLsub != $true) | ($true != $true) | ((in @ (setadjoin @ sK125 @ emptyset) @ (binintersect @ (powerset @ (binunion @ sK126 @ sK127)) @ X0)) != $true) | ((in @ (setadjoin @ sK125 @ (setadjoin @ sK128 @ emptyset)) @ (binintersect @ (powerset @ (binunion @ sK126 @ sK127)) @ X1)) != $true)) )),
% 78.40/12.31 inference(superposition,[status(thm)],[f2243,f1360])).
% 78.40/12.31 thf(f1360,plain,(
% 78.40/12.31 ( ! [X2 : $i,X3 : $i] : (((subset @ (binintersect @ X2 @ X3) @ X2) = $true) | (binintersectLsub != $true)) )),
% 78.40/12.31 inference(cnf_transformation,[status(thm)],[f714])).
% 78.40/12.31 thf(f714,plain,(
% 78.40/12.31 ((binintersectLsub = $true) | ((subset @ (binintersect @ sK52 @ sK53) @ sK52) != $true)) & (! [X2 : $i,X3 : $i] : ((subset @ (binintersect @ X2 @ X3) @ X2) = $true) | (binintersectLsub != $true))),
% 78.40/12.31 inference(skolemisation,[status(esa),new_symbols(skolem,[sK52,sK53])],[f712,f713])).
% 78.40/12.31 thf(f713,plain,(
% 78.40/12.31 ? [X0 : $i,X1 : $i] : ((subset @ (binintersect @ X0 @ X1) @ X0) != $true) => ((subset @ (binintersect @ sK52 @ sK53) @ sK52) != $true)),
% 78.40/12.31 introduced(definition,[],[choice_axiom])).
% 78.40/12.31 thf(f712,plain,(
% 78.40/12.31 ((binintersectLsub = $true) | ? [X0 : $i,X1 : $i] : ((subset @ (binintersect @ X0 @ X1) @ X0) != $true)) & (! [X2 : $i,X3 : $i] : ((subset @ (binintersect @ X2 @ X3) @ X2) = $true) | (binintersectLsub != $true))),
% 78.40/12.31 inference(rectify,[status(thm)],[f711])).
% 78.40/12.31 thf(f711,plain,(
% 78.40/12.31 ((binintersectLsub = $true) | ? [X0 : $i,X1 : $i] : ((subset @ (binintersect @ X0 @ X1) @ X0) != $true)) & (! [X0 : $i,X1 : $i] : ((subset @ (binintersect @ X0 @ X1) @ X0) = $true) | (binintersectLsub != $true))),
% 78.40/12.31 inference(nnf_transformation,[status(thm)],[f323])).
% 78.40/12.31 thf(f323,plain,(
% 78.40/12.31 (binintersectLsub = $true) <=> ! [X0 : $i,X1 : $i] : ((subset @ (binintersect @ X0 @ X1) @ X0) = $true)),
% 78.40/12.31 inference(fool_elimination,[status(thm)],[f322])).
% 78.40/12.31 thf(f322,plain,(
% 78.40/12.31 (! [X0 : $i,X1 : $i] : (subset @ (binintersect @ X0 @ X1) @ X0) = binintersectLsub)),
% 78.40/12.31 inference(rectify,[status(thm)],[f111])).
% 78.40/12.31 thf(f111,axiom,(
% 78.40/12.31 (! [X3 : $i,X4 : $i] : (subset @ (binintersect @ X3 @ X4) @ X3) = binintersectLsub)),
% 78.40/12.31 file('/export/starexec/sandbox/tmp/tmp.EC9PjZGDVh/DTF2THF_12319.p',binintersectLsub)).
% 78.40/12.31 thf(f2243,plain,(
% 78.40/12.31 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((subset @ (binintersect @ X0 @ (binunion @ X1 @ X2)) @ (powerset @ (binunion @ sK126 @ sK127))) != $true) | ((in @ (setadjoin @ sK125 @ (setadjoin @ sK128 @ emptyset)) @ (binintersect @ X0 @ X2)) != $true) | ((in @ (setadjoin @ sK125 @ emptyset) @ (binintersect @ X0 @ X1)) != $true)) )),
% 78.40/12.31 inference(subsumption_resolution,[status(thm)],[f2230,f1493])).
% 78.40/12.31 thf(f1493,plain,(
% 78.40/12.31 (bs114d = $true)),
% 78.40/12.31 inference(cnf_transformation,[status(thm)],[f834])).
% 78.40/12.31 thf(f2230,plain,(
% 78.40/12.31 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ (setadjoin @ sK125 @ (setadjoin @ sK128 @ emptyset)) @ (binintersect @ X0 @ X2)) != $true) | (bs114d != $true) | ((in @ (setadjoin @ sK125 @ emptyset) @ (binintersect @ X0 @ X1)) != $true) | ((subset @ (binintersect @ X0 @ (binunion @ X1 @ X2)) @ (powerset @ (binunion @ sK126 @ sK127))) != $true)) )),
% 78.40/12.31 inference(superposition,[status(thm)],[f2174,f1609])).
% 78.40/12.31 thf(f1609,plain,(
% 78.40/12.31 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((binunion @ (binintersect @ X3 @ X5) @ (binintersect @ X3 @ X4)) = (binintersect @ X3 @ (binunion @ X5 @ X4))) | (bs114d != $true)) )),
% 78.40/12.31 inference(cnf_transformation,[status(thm)],[f838])).
% 78.40/12.31 thf(f838,plain,(
% 78.40/12.31 ((bs114d = $true) | ((binintersect @ sK129 @ (binunion @ sK131 @ sK130)) != (binunion @ (binintersect @ sK129 @ sK131) @ (binintersect @ sK129 @ sK130)))) & (! [X3 : $i,X4 : $i,X5 : $i] : ((binunion @ (binintersect @ X3 @ X5) @ (binintersect @ X3 @ X4)) = (binintersect @ X3 @ (binunion @ X5 @ X4))) | (bs114d != $true))),
% 78.40/12.31 inference(skolemisation,[status(esa),new_symbols(skolem,[sK129,sK130,sK131])],[f836,f837])).
% 78.40/12.31 thf(f837,plain,(
% 78.40/12.31 ? [X0 : $i,X1 : $i,X2 : $i] : ((binintersect @ X0 @ (binunion @ X2 @ X1)) != (binunion @ (binintersect @ X0 @ X2) @ (binintersect @ X0 @ X1))) => ((binintersect @ sK129 @ (binunion @ sK131 @ sK130)) != (binunion @ (binintersect @ sK129 @ sK131) @ (binintersect @ sK129 @ sK130)))),
% 78.40/12.31 introduced(definition,[],[choice_axiom])).
% 78.40/12.31 thf(f836,plain,(
% 78.40/12.31 ((bs114d = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : ((binintersect @ X0 @ (binunion @ X2 @ X1)) != (binunion @ (binintersect @ X0 @ X2) @ (binintersect @ X0 @ X1)))) & (! [X3 : $i,X4 : $i,X5 : $i] : ((binunion @ (binintersect @ X3 @ X5) @ (binintersect @ X3 @ X4)) = (binintersect @ X3 @ (binunion @ X5 @ X4))) | (bs114d != $true))),
% 78.40/12.31 inference(rectify,[status(thm)],[f835])).
% 78.40/12.31 thf(f835,plain,(
% 78.40/12.31 ((bs114d = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : ((binintersect @ X0 @ (binunion @ X2 @ X1)) != (binunion @ (binintersect @ X0 @ X2) @ (binintersect @ X0 @ X1)))) & (! [X0 : $i,X1 : $i,X2 : $i] : ((binintersect @ X0 @ (binunion @ X2 @ X1)) = (binunion @ (binintersect @ X0 @ X2) @ (binintersect @ X0 @ X1))) | (bs114d != $true))),
% 78.40/12.31 inference(nnf_transformation,[status(thm)],[f433])).
% 78.40/12.31 thf(f433,plain,(
% 78.40/12.31 (bs114d = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : ((binintersect @ X0 @ (binunion @ X2 @ X1)) = (binunion @ (binintersect @ X0 @ X2) @ (binintersect @ X0 @ X1)))),
% 78.40/12.31 inference(fool_elimination,[status(thm)],[f432])).
% 78.40/12.31 thf(f432,plain,(
% 78.40/12.31 (bs114d = ! [X0 : $i,X1 : $i,X2 : $i] : ((binintersect @ X0 @ (binunion @ X2 @ X1)) = (binunion @ (binintersect @ X0 @ X2) @ (binintersect @ X0 @ X1))))),
% 78.40/12.31 inference(rectify,[status(thm)],[f119])).
% 78.40/12.31 thf(f119,axiom,(
% 78.40/12.31 (bs114d = ! [X3 : $i,X5 : $i,X4 : $i] : ((binintersect @ X3 @ (binunion @ X4 @ X5)) = (binunion @ (binintersect @ X3 @ X4) @ (binintersect @ X3 @ X5))))),
% 78.40/12.31 file('/export/starexec/sandbox/tmp/tmp.EC9PjZGDVh/DTF2THF_12319.p',bs114d)).
% 78.40/12.31 thf(f2174,plain,(
% 78.40/12.31 ( ! [X0 : $i,X1 : $i] : (((subset @ (binunion @ X0 @ X1) @ (powerset @ (binunion @ sK126 @ sK127))) != $true) | ($true != (in @ (setadjoin @ sK125 @ emptyset) @ X0)) | ((in @ (setadjoin @ sK125 @ (setadjoin @ sK128 @ emptyset)) @ X1) != $true)) )),
% 78.40/12.31 inference(subsumption_resolution,[status(thm)],[f2145,f1566])).
% 78.40/12.31 thf(f2145,plain,(
% 78.40/12.31 ( ! [X0 : $i,X1 : $i] : (((in @ (setadjoin @ sK125 @ (setadjoin @ sK128 @ emptyset)) @ X1) != $true) | ($true != (in @ (setadjoin @ sK125 @ emptyset) @ X0)) | ((subset @ (binunion @ X0 @ X1) @ (powerset @ (binunion @ sK126 @ sK127))) != $true) | (upairsubunion != $true)) )),
% 78.40/12.31 inference(trivial_inequality_removal,[status(thm)],[f2111])).
% 78.40/12.31 thf(f2111,plain,(
% 78.40/12.31 ( ! [X0 : $i,X1 : $i] : (((in @ (setadjoin @ sK125 @ (setadjoin @ sK128 @ emptyset)) @ X1) != $true) | (upairsubunion != $true) | ($true != (in @ (setadjoin @ sK125 @ emptyset) @ X0)) | ($true != $true) | ((subset @ (binunion @ X0 @ X1) @ (powerset @ (binunion @ sK126 @ sK127))) != $true)) )),
% 78.40/12.31 inference(superposition,[status(thm)],[f2107,f1339])).
% 78.40/12.31 thf(f2107,plain,(
% 78.40/12.31 ( ! [X0 : $i] : (((subset @ (setadjoin @ (setadjoin @ sK125 @ emptyset) @ (setadjoin @ (setadjoin @ sK125 @ (setadjoin @ sK128 @ emptyset)) @ emptyset)) @ X0) != $true) | ((subset @ X0 @ (powerset @ (binunion @ sK126 @ sK127))) != $true)) )),
% 78.40/12.31 inference(subsumption_resolution,[status(thm)],[f2102,f1564])).
% 78.40/12.31 thf(f1564,plain,(
% 78.40/12.31 (subsetTrans = $true)),
% 78.40/12.31 inference(cnf_transformation,[status(thm)],[f834])).
% 78.40/12.31 thf(f2102,plain,(
% 78.40/12.31 ( ! [X0 : $i] : (((subset @ (setadjoin @ (setadjoin @ sK125 @ emptyset) @ (setadjoin @ (setadjoin @ sK125 @ (setadjoin @ sK128 @ emptyset)) @ emptyset)) @ X0) != $true) | ((subset @ X0 @ (powerset @ (binunion @ sK126 @ sK127))) != $true) | (subsetTrans != $true)) )),
% 78.40/12.31 inference(trivial_inequality_removal,[status(thm)],[f2098])).
% 78.40/12.31 thf(f2098,plain,(
% 78.40/12.31 ( ! [X0 : $i] : (((subset @ (setadjoin @ (setadjoin @ sK125 @ emptyset) @ (setadjoin @ (setadjoin @ sK125 @ (setadjoin @ sK128 @ emptyset)) @ emptyset)) @ X0) != $true) | ($true != $true) | ((subset @ X0 @ (powerset @ (binunion @ sK126 @ sK127))) != $true) | (subsetTrans != $true)) )),
% 78.40/12.31 inference(superposition,[status(thm)],[f1468,f1658])).
% 78.40/12.31 thf(f1658,plain,(
% 78.40/12.31 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((subset @ X1 @ X0) = $true) | ($true != (subset @ X1 @ X2)) | (subsetTrans != $true) | ((subset @ X2 @ X0) != $true)) )),
% 78.40/12.31 inference(cnf_transformation,[status(thm)],[f896])).
% 78.40/12.31 thf(f896,plain,(
% 78.40/12.31 (! [X0 : $i,X1 : $i,X2 : $i] : (((subset @ X2 @ X0) != $true) | ($true != (subset @ X1 @ X2)) | ((subset @ X1 @ X0) = $true)) | (subsetTrans != $true)) & ((subsetTrans = $true) | (($true = (subset @ sK167 @ sK165)) & ((subset @ sK166 @ sK167) = $true) & ((subset @ sK166 @ sK165) != $true)))),
% 78.40/12.31 inference(skolemisation,[status(esa),new_symbols(skolem,[sK165,sK166,sK167])],[f894,f895])).
% 78.40/12.31 thf(f895,plain,(
% 78.40/12.31 ? [X3 : $i,X4 : $i,X5 : $i] : (((subset @ X5 @ X3) = $true) & ((subset @ X4 @ X5) = $true) & ((subset @ X4 @ X3) != $true)) => (($true = (subset @ sK167 @ sK165)) & ((subset @ sK166 @ sK167) = $true) & ((subset @ sK166 @ sK165) != $true))),
% 78.40/12.31 introduced(definition,[],[choice_axiom])).
% 78.40/12.31 thf(f894,plain,(
% 78.40/12.31 (! [X0 : $i,X1 : $i,X2 : $i] : (((subset @ X2 @ X0) != $true) | ($true != (subset @ X1 @ X2)) | ((subset @ X1 @ X0) = $true)) | (subsetTrans != $true)) & ((subsetTrans = $true) | ? [X3 : $i,X4 : $i,X5 : $i] : (((subset @ X5 @ X3) = $true) & ((subset @ X4 @ X5) = $true) & ((subset @ X4 @ X3) != $true)))),
% 78.40/12.31 inference(rectify,[status(thm)],[f893])).
% 78.40/12.31 thf(f893,plain,(
% 78.40/12.31 (! [X0 : $i,X1 : $i,X2 : $i] : (((subset @ X2 @ X0) != $true) | ($true != (subset @ X1 @ X2)) | ((subset @ X1 @ X0) = $true)) | (subsetTrans != $true)) & ((subsetTrans = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (((subset @ X2 @ X0) = $true) & ($true = (subset @ X1 @ X2)) & ((subset @ X1 @ X0) != $true)))),
% 78.40/12.31 inference(nnf_transformation,[status(thm)],[f531])).
% 78.40/12.31 thf(f531,plain,(
% 78.40/12.31 ! [X0 : $i,X1 : $i,X2 : $i] : (((subset @ X2 @ X0) != $true) | ($true != (subset @ X1 @ X2)) | ((subset @ X1 @ X0) = $true)) <=> (subsetTrans = $true)),
% 78.40/12.31 inference(flattening,[status(thm)],[f530])).
% 78.40/12.31 thf(f530,plain,(
% 78.40/12.31 ! [X0 : $i,X1 : $i,X2 : $i] : ((((subset @ X1 @ X0) = $true) | ((subset @ X2 @ X0) != $true)) | ($true != (subset @ X1 @ X2))) <=> (subsetTrans = $true)),
% 78.40/12.31 inference(ennf_transformation,[status(thm)],[f184])).
% 78.40/12.31 thf(f184,plain,(
% 78.40/12.31 ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (subset @ X1 @ X2)) => (((subset @ X2 @ X0) = $true) => ((subset @ X1 @ X0) = $true))) <=> (subsetTrans = $true)),
% 78.40/12.31 inference(fool_elimination,[status(thm)],[f183])).
% 78.40/12.31 thf(f183,plain,(
% 78.40/12.31 (subsetTrans = ! [X0 : $i,X1 : $i,X2 : $i] : ((subset @ X1 @ X2) => ((subset @ X2 @ X0) => (subset @ X1 @ X0))))),
% 78.40/12.31 inference(rectify,[status(thm)],[f89])).
% 78.40/12.31 thf(f89,axiom,(
% 78.40/12.31 (subsetTrans = ! [X5 : $i,X3 : $i,X4 : $i] : ((subset @ X3 @ X4) => ((subset @ X4 @ X5) => (subset @ X3 @ X5))))),
% 78.40/12.31 file('/export/starexec/sandbox/tmp/tmp.EC9PjZGDVh/DTF2THF_12319.p',subsetTrans)).
% 78.40/12.31 thf(f1468,plain,(
% 78.40/12.31 ($true != (subset @ (setadjoin @ (setadjoin @ sK125 @ emptyset) @ (setadjoin @ (setadjoin @ sK125 @ (setadjoin @ sK128 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ sK126 @ sK127))))),
% 78.40/12.31 inference(cnf_transformation,[status(thm)],[f834])).
% 78.40/12.31 % SZS output end Proof for DTF2THF_12319
% 78.40/12.31 % (12821)------------------------------
% 78.40/12.31 % (12821)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 78.40/12.31 % (12821)Termination reason: Refutation
% 78.40/12.31
% 78.40/12.31 % (12821)Memory used [KB]: 12025
% 78.40/12.31 % (12821)Time elapsed: 1.293 s
% 78.40/12.31 % (12821)Instructions burned: 4133 (million)
% 78.40/12.31 % (12821)------------------------------
% 78.40/12.31 % (12821)------------------------------
% 78.40/12.31 % (12581)Success in time 10.844 s
%------------------------------------------------------------------------------